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Publications on CSC sorted by year


Ü. V. Çatalyürek,
C. Aykanat,
and B. Uçar.
On twodimensional sparse matrix partitioning: Models, methods, and a recipe.
SIAM Journal on Scientific Computing,
32(2):656683,
2010.
Keyword(s): Sparse matrixvector multiplication,
Hypergraph partitioning,
Hypergraph model,
Communication cost.
[bibtexkey = caau:10]

R. A. Brualdi and D. M. Cvetkovic.
A Combinatorial Approach to Matrix Theory and its Applications.
Chapman & Hall/CRC Press,
Boca Raton,
2009.
Keyword(s): Matrix power,
Determinant,
Matrix inverse,
Linear system solution.
[bibtexkey = brcv:09]

R. Burkard,
M. Dell'Amico,
and S. Martello.
Assignment Problems.
SIAM,
Philadelphia, PA, USA,
2009.
[bibtexkey = budm:09]

M. Manguoglu,
A. Sameh,
and O. Schenk.
PSPIKE: Parallel sparse linear system solver.
In In Proc. EuroPar 2009 Parallel Processing,
pages 797808,
2009.
[bibtexkey = mass:09]

R. H. Bisseling.
Combinatorial problems in highperformance computing.
Presentation at Dagstuhl Seminar on Combinatorial Scientific Computing (09061),
February 2009.
[bibtexkey = biss:09]

A. Pothen.
Graph matchings in combinatorial scientific computing (Vertexweighted and parallel edgeweighted).
Presentation at Dagstuhl Seminar on Combinatorial Scientific Computing (09061),
February 2009.
[bibtexkey = poth:09]

E. Agullo.
On the outofcore factorization of large sparse matrices.
PhD thesis,
Ecole Normale Supérieure de Lyon,
Lyon, France,
2008.
[bibtexkey = agul:08]

M. Halappanavar.
Algorithms for VertexWeighted Matching in Graphs.
PhD thesis,
Old Dominion University,
Norfolk, Virginia, USA,
2008.
[bibtexkey = maha:09]

E. Agullo,
A. Guermouche,
and J.Y. L'Excellent.
A parallel outofcore multifrontal method: Storage of factors on disk and analysis of models for an outofcore active memory.
Parallel Computing,
34(68):296317,
2008.
Keyword(s): Outofcore factorization,
Multifrontal method.
[bibtexkey = aggl:08]

M. Elkin,
Y. Emek,
D. A. Spielman,
and S.H. Teng.
Lowerstretch spanning trees.
SIAM Journal on Computing,
38(2):608628,
2008.
[bibtexkey = eest:08]

P. Hénon,
P. Ramet,
and J. Roman.
On finding approximate supernodes for an efficient blockILU(k) factorization.
Parallel Computing,
34(68):345362,
2008.
[bibtexkey = herr:08]

H. de Sterck,
R. D. Falgout,
J. W. Nolting,
and U. M. Yang.
Distancetwo interpolation for parallel algebraic multigrid.
Numerical Linear Algebra with Applications,
15(23):115139,
MARAPR 2008.
[bibtexkey = sfny:08]

F. Manne and R. H. Bisseling.
A parallel approximation algorithm for the weighted maximum matching problem.
In Roman Wyrzykowski,
Konrad Karczewski,
Jack Dongarra,
and Jerzy Wasniewski, editors,
Parallel Processing and Applied Mathematics,
volume 4967 of Lecture Notes in Computer Science,
pages 708717,
2008.
[bibtexkey = mabi:07]

S. Toledo and A. Uchitel.
A supernodal outofcore sparse Gaussianelimination method.
In Roman Wyrzykowski,
Konrad Karczewski,
Jack Dongarra,
and Jerzy Wasniewski, editors,
7th International Conference on Parallel Processing and Applied Mathematics (PPAM 2007),,
volume 4967 of Lecture Notes in Computer Science,
pages 728737,
2008.
SpringerVerlag Berlin Heidelberg.
[bibtexkey = touc:08]

J. K. Reid and J. A. Scott.
An efficient outofcore sparse symmetric indefinite direct solver.
Technical report RALTR2008024,
Computational Sciences and Engineering Department, Rutherford Appleton Laboratory,
Oxon, OX11 0QX, England,
December 2008.
[bibtexkey = resc:08]

F. Pellegrini.
SCOTCH 5.1 User's Guide.
Laboratoire Bordelais de Recherche en Informatique (LaBRI),
2008.
Keyword(s): Graph partitioning,
Sparse matrix ordering,
Nested dissection.
[bibtexkey = pell:08:scotch]

I. S. Duff,
D. Ruiz,
and B. Uçar.
Computing a class of bipartite matchings in parallel.
Presentation at SIAM 13th Conference on Parallel Processing for Scientific Computing (PP08), Atlanta, GA, USA,
March 2008.
Keyword(s): Matching.
[bibtexkey = duru:08]

I. Koutis.
Combinatorial and algebraic tools for multigrid algorithms.
PhD thesis,
Carnegie Mellon University,
Pittsburgh,
May 2007.
[bibtexkey = kout:07]

D. M. Alber and L. N. Olson.
Parallel coarsegrid selection.
Numerical Linear Algebra with Applications,
14(8):611643,
2007.
Keyword(s): Algebraic multigrid,
Preconditioning.
[bibtexkey = alol:07]

D. Fritzsche,
A. Frommer,
and D. B. Szyld.
Extensions of certain graphbased algorithms for preconditioning.
SIAM Journal on Scientific Computing,
29(5):21442161,
2007.
[bibtexkey = frfs:07]

S. Maclachlan and Y. Saad.
A greedy strategy for coarsegrid selection.
SIAM Journal on Scientific Computing,
29(5):18251853,
2007.
[bibtexkey = masa:07]

B. Uçar and C. Aykanat.
Partitioning sparse matrices for parallel preconditioned iterative methods.
SIAM Journal on Scientific Computing,
29(4):16831709,
2007.
Keyword(s): Sparse matrixvector multiplication,
Hypergraph partitioning,
Hypergraph model,
Preconditioning,
Multiphysics simulation,
Multimesh simulation,
Communication cost.
[bibtexkey = ucay:07a]

E. Agullo,
A. Guermouche,
and J.Y. L'Excellent.
Reducing the I/O volume in an outofcore sparse multifrontal solver.
In S. Aluru,
M. Parashar,
R. Badrinath,
and V. K. Prasanna, editors,
High Performance Computing  HiPC2007; 14th International Conference,
volume 4873 of Lecture Notes in Computer Science,
pages 260280,
2007.
Keyword(s): Outofcore factorization,
Multifrontal method,
Task scheduling,
Elimination tree.
[bibtexkey = aggl:07]

B. Hendrickson and A. Pothen.
Combinatorial scientific computing: The enabling power of discrete algorithms in computational science.
In M. Dayde,
M. L. M. Palma,
L. G. A. Coutinho,
E. Pacitti,
and J. C. Lopes, editors,
High Performance Computing for Computational ScienceVECPAR 2006,
volume 4395 of Lecture Notes in Computer Science,
pages 260280,
2007.
Keyword(s): Minimum degree ordering algorithm,
Coloring,
Jacobian matrix,
Sparse Hessian matrix.
[bibtexkey = hepo:07]

R. A. Brualdi.
Combinatorial Matrix Classes,
volume 108 of Encyclopedia of Mathematics and its Applications.
Cambridge University Press,
2006.
[bibtexkey = brua:06]

T. A. Davis.
Direct Methods for Sparse Linear Systems,
number 2 of Fundamentals of Algorithms.
Society for Industrial and Applied Mathematics,
Philadelphia, PA, USA,
2006.
[bibtexkey = davi:06]

E. Chow,
R. D. Falgout,
J. J. Hu,
R. S. Tuminaro,
and U. M. Yang.
A survey of parallelization techniques for multigrid solvers.
In M. A. Heroux,
P. Raghavan,
and H. D. Simon, editors, Parallel Processing for Scientific Computing,
volume 20 of Software, Environments, and Tools,
chapter 10,
pages 179201.
SIAM,
2006.
[bibtexkey = cfht:06]

K. D. Devine,
E. G. Boman,
and G. Karypis.
Partitioning and load balancing for emerging parallel applications and architectures.
In M. Heroux,
A. Raghavan,
and H. Simon, editors, Frontiers of Scientific Computing.
SIAM,
Philadelphia,
2006.
[bibtexkey = debk:06]

P. R. Amestoy,
A. Guermouche,
J.Y. L'Excellent,
and S. Pralet.
Hybrid scheduling for the parallel solution of linear systems.
Parallel Computing,
32(2):136156,
2006.
[bibtexkey = aglp:06]

M. Bern,
J. R. Gilbert,
B. Hendrickson,
N. Nguyen,
and S. Toledo.
Supportgraph preconditioners.
SIAM Journal on Matrix Analysis and Applications,
27(4):930951,
2006.
[bibtexkey = bghn:06]

M. Bollhöfer and O. Schenk.
Combinatorial aspects in sparse elimination methods.
GAMM Mitteilungen,
29:342367,
2006.
[bibtexkey = bosh:06]

A. Guermouche and J.Y. L'Excellent.
Constructing memoryminimizing schedules for multifrontal methods.
ACM Transactions on Mathematical Software,
32(1):1732,
2006.
[bibtexkey = gule:06]

I. Lee,
P. Raghavan,
and E. G. Ng.
Effective preconditioning through ordering interleaved with incomplete factorization.
SIAM Journal on Matrix Analysis and Applications,
27(4):10691088,
2006.
[bibtexkey = lern:06]

O. Meshar,
D. Irony,
and S. Toledo.
An outofcore sparse symmetricindefinite factorization method.
ACM Transactions on Mathematical Software,
32(3):445471,
2006.
[bibtexkey = meit:06]

H. de Sterck,
U. M. Yang,
and J. J. Heys.
Reducing complexity in parallel algebraic multigrid preconditioners.
SIAM Journal on Matrix Analysis and Applications,
27(4):10191039,
2006.
[bibtexkey = styh:06]

M. W. Gee,
C. M. Siefert,
J. J. Hu,
R. S. Tuminaro,
and M. G. Sala.
ML 5.0 smoothed aggregation user's guide.
Technical report SAND20062649,
Sandia National Laboratories,
2006.
[bibtexkey = mlguide:06]

J. K. Reid and J. A. Scott.
An outofcore sparse Cholesky solver.
Technical report RALTR2006013,
Computational Sciences and Engineering Department, Rutherford Appleton Laboratory,
Oxon, OX11 0QX, England,
2006.
[bibtexkey = resc:06b]

R. H. Bisseling and W. Meesen.
Communication balancing in parallel sparse matrixvector multiplication.
Electronic Transactions on Numerical Analysis,
21,
2005.
Keyword(s): Sparse matrixvector multiplication,
Parallel computing,
Bulk synchronous parallel.
[bibtexkey = bime:06]

I. S. Duff and S. Pralet.
Strategies for scaling and pivoting for sparse symmetric indefinite problems.
SIAM Journal on Matrix Analysis and Applications,
27(2):313340,
2005.
[bibtexkey = dupr:05]

S. C. Eisenstat and J. W. H. Liu.
A treebased dataflow model for the unsymmetric multifrontal method.
Electronic Transactions on Numerical Analysis,
21:119,
2005.
[bibtexkey = eili:05b]

S. C. Eisenstat and J. W. H. Liu.
The theory of elimination trees for sparse unsymmetric matrices.
SIAM Journal on Matrix Analysis and Applications,
26(3):686705,
2005.
[bibtexkey = eili:05]

A. H. Gebremedhin,
F. Manne,
and A. Pothen.
What color is your Jacobian? Graph coloring for computing derivatives.
SIAM Review,
47(4):629705,
2005.
[bibtexkey = gemp:05]

H. W. Kuhn.
Statement for Naval Research Logistics.
Naval Research Logistics,
52(1):6,
2005.
[bibtexkey = kuhn:05b]

H. W. Kuhn.
The Hungarian method for the assignment problem.
Naval Research Logistics,
52(1):721,
2005.
[bibtexkey = kuhn:05]

Y. Saad.
Multilevel ILU with reorderings for diagonal dominance.
SIAM Journal on Scientific Computing,
27(3):10321057,
2005.
[bibtexkey = saad:05]

D. Bozdag,
Ü. V. Çatalyürek,
A. H. Gebremedhin,
F. Manne,
E. G. Boman,
and F. Özgüner.
A parallel distance2 graph coloring algorithm for distributed memory computers.
In L. T. Yang,
O. F. Rana,
B. Di Martino,
and J. Dongarra, editors,
Proceedings of 2005 International Conference on High Performance Computing and Communications (HPCC05),
volume 3726 of Lecture Notes in Computer Science,
pages 796806,
2005.
[bibtexkey = bcgm:05]

M. Sala and M. Heroux.
Robust algebraic preconditioners with IFPACK 3.0.
Technical report SAND0662,
Sandia National Laboratories,
2005.
[bibtexkey = ifpackguide]

R. H. Bisseling.
Parallel Scientific Computation: A Structured Approach using BSP and MPI.
Oxford University Press, Oxford, UK,
March 2004.
Keyword(s): Sparse matrixvector multiplication,
Fast Fourier Transform,
Wavelet,
Bulk synchronous parallel,
Parallel computing,
Message passing interface.
[bibtexkey = biss:04]

P. R. Amestoy,
I. S. Duff,
and C. Vömel.
Task scheduling in an asynchronous distributed memory multifrontal solver.
SIAM Journal on Matrix Analysis and Applications,
26(2):544565,
2004.
[bibtexkey = amdv:04]

E. G. Boman,
D. Chen,
B. Hendrickson,
and S. Toledo.
Maximumweightbasis preconditioners.
Numerical Linear Algebra with Applications,
11(89):695721,
2004.
[bibtexkey = bchs:04]

V. Rotkin and S. Toledo.
The design and implementation of a new outofcore sparse Cholesky factorization method.
ACM Transactions on Mathematical Software,
30(1):1946,
2004.
[bibtexkey = roto:04]

D. A. Spielman and S.H. Teng.
Nearlylinear time algorithms for graph partitioning, graph sparsification, and solving linear systems.
In STOC'04: Proceedings of the 36th annual ACM symposium on Theory of computing,
New York, NY, USA,
pages 8190,
2004.
ACM.
[bibtexkey = spte:04]

J. Riedy and J. Demmel.
Parallel weighted bipartite matching and applications.
Presentation at SIAM 11th Conference on Parallel Processing for Scientific Computing (PP04), San Francisco, CA, USA,
February 2004.
Keyword(s): Matching.
[bibtexkey = ride:04]

Y. Saad.
Iterative Methods for Sparse Linear Systems.
SIAM,
Philadelphia,
2nd edition,
2003.
[bibtexkey = saad:03]

E. G. Boman and B. Hendrickson.
Support theory for preconditioning.
SIAM Journal on Matrix Analysis and Applications,
25(3):694717,
2003.
[bibtexkey = bohe:03]

D. Chen and S. Toledo.
Vaidya's preconditioners: Implementation and experimental study.
Electronic Transactions on Numerical Analysis,
16:3049,
2003.
[bibtexkey = chto:03]

A. Guermouche,
J.Y. L'Excellent,
and G. Utard.
Impact of reordering on the memory of a multifrontal solver.
Parallel Computing,
29(9):11911218,
2003.
[bibtexkey = gulu:03]

H. Kim,
J. Xu,
and L. Zikatanov.
A multigrid method based on graph matching for convectiondiffusion equations.
Numerical Linear Algebra with Applications,
10(12):181195,
2003.
Keyword(s): Matching,
Algebraic multigrid,
Preconditioning.
[bibtexkey = kixz:03]

Y. Saad.
Finding exact and approximate block structures for ILU preconditioning.
SIAM Journal on Scientific Computing,
24(4):11071123,
2003.
[bibtexkey = saad:03b]

D. A. Spielman and S.H. Teng.
Solving sparse, symmetric, diagonally dominant linear systems in time $\mathcal{O}(m^{1.31})$.
In 44th Annual IEEE Symposium on Foundations of Computer Science,
pages 416427,
2003.
IEEE.
[bibtexkey = spte:03]

M. Benzi.
Preconditioning techniques for large linear systems: A survey.
Journal of Computational Physics,
182(2):418477,
2002.
[bibtexkey = benz:02]

A. Gupta.
Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices.
SIAM Journal on Matrix Analysis and Applications,
24(2):529552,
2002.
[bibtexkey = gupt:02]

V. E. Henson and U. M. Yang.
BoomerAMG: A parallel algebraic multigrid solver and preconditioner.
Applied Numerical Mathematics,
41(1):155177,
2002.
[bibtexkey = heya:02]

C. Walshaw.
The Parallel JOSTLE Library User's Guide, Version 3.0.
University of Greenwich,
London, UK,
2002.
[bibtexkey = wals:02:jostle]

F. Dobrian.
External Memory Algorithms for Factoring Sparse Matrices.
PhD thesis,
Old Dominion University,
Norfolk, Virginia, USA,
2001.
[bibtexkey = dobr:01]

P. R. Amestoy,
I. S. Duff,
J.Y. L'Excellent,
and J. Koster.
A fully asynchronous multifrontal solver using distributed dynamic scheduling.
SIAM Journal on Matrix Analysis and Applications,
23(1):1541,
2001.
[bibtexkey = adlk:01]

M. Bollhöfer.
A robust ILU with pivoting based on monitoring the growth of the inverse factors.
Linear Algebra and its Applications,
338(13):201218,
2001.
[bibtexkey = boll:01]

R. Bridson and W.P. Tang.
A structural diagnosis of some IC orderings.
SIAM Journal on Scientific Computing,
22(5):15271532,
2001.
[bibtexkey = brta:01]

I. S. Duff and J. Koster.
On algorithms for permuting large entries to the diagonal of a sparse matrix.
SIAM Journal on Matrix Analysis and Applications,
22:973996,
2001.
[bibtexkey = duko:01]

D. Hysom and A. Pothen.
A scalable parallel algorithm for incomplete factor preconditioning.
SIAM Journal on Scientific Computing,
22(6):21942215,
2001.
[bibtexkey = hypo:01]

J. Schulze.
Towards a tighter coupling of bottomup and topdown sparse matrix ordering methods.
BIT Numerical Mathematics,
41(4):800841,
2001.
[bibtexkey = schu:01]

K. Stüben.
A review of algebraic multigrid.
Journal of Computational and Applied Mathematics,
128(12):281309,
2001.
[bibtexkey = stub:01]

Ü. V. Çatalyürek and C. Aykanat.
A finegrain hypergraph model for $2$D decomposition of sparse matrices.
In Proceedings of the 15th International Parallel and Distributed Processing Symposium (IPDPS,
San Francisco, CA,
2001.
Keyword(s): Sparse matrixvector multiplication,
Hypergraph partitioning,
Hypergraph model,
Communication cost.
[bibtexkey = caay:01]

P. Heggernes,
S. C. Eisenstat,
G. Kumfert,
and A. Pothen.
The computational complexity of the minimum degree algorithm.
In Proceedings of NIK 200114th Norwegian Computer Science Conference,
Tromso, Norway,
pages 98109,
2001.
[bibtexkey = hekp:01]

R. S. Varga.
Matrix Iterative Analysis.
Springer, Berlin, Heidelberg, New York,
Second edition,
2000.
[bibtexkey = varg:00]

P. R. Amestoy,
I. S. Duff,
and J.Y. L'Excellent.
Multifrontal parallel distributed symmetric and unsymmetric solvers.
Computer methods in applied mechanics and engineering,
184(24):501520,
2000.
[bibtexkey = amde:00]

M. Benzi,
J. C. Haws,
and M. Tůma.
Preconditioning highly indefinite and nonsymmetric matrices.
SIAM Journal on Scientific Computing,
22(4):13331353,
2000.
[bibtexkey = beht:00]

M. Benzi and M. Tůma.
Orderings for factorized sparse approximate inverse preconditioners.
SIAM Journal on Scientific Computing,
21(5):18511868,
2000.
[bibtexkey = betu:00]

E. Chow.
A priori sparsity patterns for parallel sparse approximate inverse preconditioners.
SIAM Journal on Scientific Computing,
21(5):18041822,
2000.
[bibtexkey = chow:00]

B. Hendrickson and T. G. Kolda.
Graph partitioning models for parallel computing.
Parallel Computing,
26(12):15191534,
2000.
Keyword(s): Graph algorithms,
Graph partitioning,
Hypergraph partitioning,
Parallel computing,
Communication cost.
[bibtexkey = heko:00]

R. S. Tuminaro and C. Tong.
Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines.
In Supercomputing '00: Proceedings of the 2000 ACM/IEEE conference on Supercomputing (CDROM),
Washington, DC, USA,
pages 5,
2000.
IEEE Computer Society.
[bibtexkey = tuto:00]

G. A. Meurant.
Computer Solution of Large Linear Systems,
volume 28 of Studies in Mathematics and Its Applications.
NorthHolland,
Amsterdam, Netherlands,
1999.
[bibtexkey = meur:99]

E. G. Ng,
B. W. Peyton,
and P. Raghavan.
A blocked incomplete Cholesky preconditioner for hierarchicalmemory computers.
In D. R. Kincaid and A. C. Elster, editors, Iterative methods in scientific computation IV,
volume 5 of IMACS Series in Computational Applied Mathematics,
pages 211222.
IMACS,
New Brunswick, NJ, USA,
1999.
[bibtexkey = ngpr:99]

Ü. V. Çatalyürek and C. Aykanat.
Hypergraphpartitioningbased decomposition for parallel sparsematrix vector multiplication.
IEEE Transactions on Parallel and Distributed Systems,
10(7):673693,
July 1999.
Keyword(s): Sparse matrixvector multiplication,
Hypergraph partitioning,
Hypergraph model,
Communication cost.
[bibtexkey = caay:99]

M. Benzi,
D. B. Szyld,
and A. van Duin.
Orderings for incomplete factorization preconditioning of nonsymmetric problems.
SIAM Journal on Scientific Computing,
20(5):16521670,
1999.
[bibtexkey = besd:99]

J. W. Demmel,
S. C. Eisenstat,
J. R. Gilbert,
X. S. Li,
and J. W. H. Liu.
A supernodal approach to sparse partial pivoting.
SIAM Journal on Matrix Analysis and Applications,
20(3):720755,
1999.
[bibtexkey = degll:99]

I. S. Duff and J. Koster.
The design and use of algorithms for permuting large entries to the diagonal of sparse matrices.
SIAM Journal on Matrix Analysis and Applications,
20(4):889901,
1999.
[bibtexkey = duko:99]

I. S. Duff and H. A. van der Vorst.
Developments and trends in the parallel solution of linear systems.
Parallel Computing,
25(1314):19311970,
1999.
[bibtexkey = duvo:99]

J. R. Gilbert and S. Toledo.
Highperformance outofcore sparse LU factorization.
In 9th SIAM Conference on Parallel Processing for Scientific Computing (CDROM),
pages p.10,
1999.
[bibtexkey = gito:99]

Ü. V. Çatalyürek and C. Aykanat.
PaToH: A multilevel hypergraph partitioning tool, Version 3.0.
Bilkent University, Department of Computer Engineering,
Ankara, 06533 Turkey. PaToH is available at http://bmi.osu.edu/umit/software.htm,
1999.
Keyword(s): Hypergraph partitioning.
[bibtexkey = caay:99a]

C. Ashcraft and J. W. H. Liu.
Robust ordering of sparse matrices using multisection.
SIAM Journal on Matrix Analysis and Applications,
19(3):816832,
1998.
Keyword(s): Sparse matrix ordering,
Minimum degree algorithm,
Nested dissection.
[bibtexkey = aslu:98]

B. Hendrickson and E. Rothberg.
Improving the run time and quality of nested dissection ordering.
SIAM Journal on Scientific Computing,
20(2):468489,
1998.
Keyword(s): Sparse matrix ordering,
Nested dissection,
Minimum degree algorithm,
Minimum degree ordering,
Graph algorithms,
Graph partitioning.
[bibtexkey = hero:98]

J. H. Reif.
Efficient approximate solution of sparse linear systems.
Computers and Mathematics with Applications,
36(9):3758,
November 1998.
[bibtexkey = reif:98]

G. Karypis and V. Kumar.
MeTiS: A software package for partitioning unstructured graphs, partitioning meshes, and computing fillreducing orderings of sparse matrices version 4.0.
University of Minnesota, Department of Comp. Sci. and Eng., Army HPC Research Center,
Minneapolis,
1998.
Keyword(s): Graph partitioning,
Sparse matrix ordering,
Nested dissection.
[bibtexkey = kaku:98:metis]

C. Ashcraft and J. W. H. Liu.
Using domain decomposition to find graph bisectors.
BIT,
37(3):506534,
1997.
[bibtexkey = aslu:97]

E. Chow and Y. Saad.
Experimental study of ILU preconditioners for indefinite matrices.
Journal of Computational and Applied Mathematics,
86(2):387414,
1997.
[bibtexkey = chsa:97]

T. A. Davis and I. S. Duff.
An unsymmetricpattern multifrontal method for sparse LU factorization.
SIAM Journal on Matrix Analysis and Applications,
18(1):140158,
1997.
[bibtexkey = dadu:97]

M. J. Grote and T. Huckle.
Parallel preconditioning with sparse approximate inverses.
SIAM Journal on Scientific Computing,
18(3):838853,
1997.
[bibtexkey = grhu:97]

G. Karypis and V. Kumar.
Parallel thresholdbased ILU factorization.
In Supercomputing '97: Proceedings of the 1997 ACM/IEEE conference on Supercomputing (CDROM),
New York, NY, USA,
pages 124,
1997.
ACM.
[bibtexkey = kaku:97]

S. Guattery.
Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners.
Technical report ICASE Report No.9747,
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center,
Hampton, Virginia,
1997.
[bibtexkey = guat:97]

K. D. Gremban.
Combinatorial Preconditioners for Sparse, Symmetric, Diagonally Dominant Linear Systems.
PhD thesis,
School of Computer Science, Carnegie Mellon University,
Pittsburgh, PA, USA,
1996.
[bibtexkey = grem:96]

A. Joshi.
Topics in Optimization and Sparse Linear Systems.
PhD thesis,
Department of Computer Science, University of Illinois UrbanaChampaign,
Urbana, IL, USA,
December 1996.
[bibtexkey = josh:96]

P. R. Amestoy,
T. A. Davis,
and I. S. Duff.
An approximate minimum degree ordering algorithm.
SIAM Journal on Matrix Analysis and Applications,
17(4):886905,
1996.
Keyword(s): Sparse matrix ordering,
Minimum degree algorithm.
[bibtexkey = amdd:96]

M. Benzi,
C. D. Meyer,
and M. Tůma.
A sparse approximate inverse preconditioner for the conjugate gradient method.
SIAM Journal on Scientific Computing,
17(5):11351149,
1996.
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M. Olschowka and A. Neumaier.
A new pivoting strategy for Gaussian elimination.
Linear Algebra and Its Applications,
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C. Ashcraft and J. W. H. Liu.
A partition improvement algorithm for generalized nested dissection.
Technical report BCSTECH94020,
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A. Gupta.
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Technical report RC 20496 (90799),
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C. Ashcraft.
Compressed graphs and the minimum degree algorithm.
SIAM Journal on Scientific Computing,
16:14041411,
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Keyword(s): Minimum degree algorithm.
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S. S. Clift and W.P. Tang.
Weighted graph based ordering techniques for preconditioned conjugate gradient methods.
BIT Numerical Mathematics,
35(1):3047,
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K. D. Gremban,
G. L. Miller,
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Performance evaluation of a parallel preconditioner.
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B. Hendrickson and R. Leland.
A multilevel algorithm for partitioning graphs.
In Supercomputing '95: Proceedings of the 1995 ACM/IEEE conference on Supercomputing (CDROM),
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B. Hendrickson and R. Leland.
The Chaco user's guide, version 2.0.
Sandia National Laboratories,
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Keyword(s): Graph partitioning,
Sparse matrix ordering,
Nested dissection.
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O. Axelsson.
Iterative solution methods.
Cambridge University Press,
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V. Kumar,
A. Grama,
A. Gupta,
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Introduction to Parallel Computing: Desing and Analysis of Algorithms.
The Benjamin/Cummings Publishing Company, Inc.,
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S. Barnard and H. D. Simon.
A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems.
Concurrency: Practice and Experience,
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Y. Saad.
ILUT: A dual threshold incomplete LU factorization.
Numerical Linear Algebra with Applications,
1(4):387402,
1994.
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M. V. Bhat,
W. G. Habashi,
J. W. H. Liu,
V. N. Nguyen,
and M. F. Peeters.
A note on nested dissection for rectangular grids.
SIAM Journal on Matrix Analysis and Applications,
14(1):253258,
1993.
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J. R. Gilbert and J. W. H. Liu.
Elimination structures for unsymmetric sparse $LU$ factors.
SIAM Journal on Matrix Analysis and Applications,
14(2):334352,
1993.
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J. W. H. Liu,
E. G. Ng,
and B. W. Peyton.
On finding supernodes for sparse matrix computations.
SIAM Journal on Matrix Analysis and Applications,
14(1):242252,
1993.
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A. Pothen and C. Sun.
A mapping algorithm for parallel sparse Cholesky factorization.
SIAM Journal on Scientific Computing,
14(5):12531257,
1993.
Keyword(s): Multifrontal method,
Cholesky factorization,
Task scheduling,
Proportional mapping.
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R. H. Bisseling.
Parallel Iterative Solution of Sparse Linear Systems on a Transputer Network.
In A. E. Fincham and B. Ford, editors,
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volume 46 of The Institute of Mathematics and its Applications Conference Series. New Series,
pages 253271,
1993.
Oxford University Press, Oxford, UK.
Keyword(s): GMRES,
Cyclic distribution,
Sparse matrixvector multiplication,
Communication cost.
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T. N. Bui and C. Jones.
A heuristic for reducing fillin in sparse matrix factorization.
In 6th SIAM Conference on Parallel Processing for Scientific Computing,
Norfolk, Virginia, USA,
pages 445452,
1993.
Keyword(s): Graph partitioning,
Multilevel algorithm.
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M. Marcus and H. Minc.
A Survey of Matrix Theory and Matrix Inequalities.
Dover,
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R. A. Brualdi.
The symbiotic relationship of combinatorics and matrix theory.
Linear Algebra and its Applications,
162164:65105,
1992.
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E. F. D'Azevedo,
P. A. Forsyth,
and W.P. Tang.
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems.
SIAM Journal on Matrix Analysis and Applications,
13(3):944961,
1992.
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E. F. D'Azevedo,
P. A. Forsyth,
and W.P. Tang.
Towards a costeffective ILU preconditioner with high level fill.
BIT Numerical Mathematics,
32(3):442463,
1992.
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J. R. Gilbert,
C. Moler,
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Sparse matrices in MATLAB: Design and implementation.
SIAM Journal on Matrix Analysis and Applications,
13:333356,
1992.
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J. R. Gilbert and R. Schreiber.
Highly parallel sparse Cholesky factorization.
SIAM Journal on Scientific and Statistical Computing,
13(5):11511172,
1992.
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R. Greenlaw.
A model classifying algorithms as inherently sequential with applications to graph searching.
Information and Computation,
97(2):133149,
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J. W. H. Liu.
The multifrontal method for sparse matrix solution: Theory and practice.
SIAM Review,
34(1):82109,
1992.
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R. A. Brualdi and H. J. Ryser.
Combinatorial Matrix Theory,
volume 39 of Encyclopedia of Mathematics and its Applications.
Cambridge University Press,
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H. Alt,
N. Blum,
K. Mehlhorn,
and M. Paul.
Computing a maximum cardinality matching in a bipartite graph in time $\mathcal{O}(n^{1.5}\sqrt{m/\log n})$.
Information Processing Letters,
37(4):237240,
1991.
Keyword(s): Matching.
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M. T. Heath,
E. Ng,
and B. W. Peyton.
Parallel algorithms for sparse linear systems.
SIAM Review,
33(3):420460,
1991.
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P. M. Vaidya.
Solving linear equations with symmetric diagonally dominant matrices by constructing good preconditioners.
Note: Unpublished manuscript presented at the IMA Workshop on Graph Theory and Sparse Matrix Computation,
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T. H. Cormen,
C. E. Leiserson,
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Introduction to Algorithms.
MIT Press,
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1990.
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J. J. Dongarra,
J. Du Croz,
I. S. Duff,
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A set of level 3 Basic Linear Algebra Subprograms..
ACM Transactions on Mathematical Software,
16:117,
1990.
Note: Http://www.netlib.org/blas/blas3paper.ps.
Keyword(s): BLAS,
Linear algebra.
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J. W. H. Liu.
The role of elimination trees in sparse factorization.
SIAM Journal on Matrix Analysis and Applications,
11(1):134172,
1990.
Keyword(s): Elimination tree,
Cholesky factorization,
Sparse matrix ordering,
Symbolic factorization.
[bibtexkey = liu:90]

J. O'Neil and D. B. Szyld.
A block ordering method for sparse matrices.
SIAM Journal on Scientific and Statistical Computing,
11(5):811823,
1990.
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A. Pothen and C.J. Fan.
Computing the block triangular form of a sparse matrix.
ACM Transactions on Mathematical Software,
16:303324,
1990.
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A. Pothen,
H. D. Simon,
and K.P. Liou.
Partitioning sparse matrices with eigenvectors of graphs.
SIAM Journal on Matrix Analysis and Applications,
11(3):430452,
1990.
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C. Ashcraft and R. Grimes.
The influence of relaxed supernode partitions on the multifrontal method.
ACM Transactions on Mathematical Software,
15(4):291309,
1989.
Keyword(s): Multifrontal method,
Supernode,
Fundamental supernode,
Relaxed supernode.
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I. S. Duff and G. A. Meurant.
The effect of ordering on preconditioned conjugate gradients.
BIT,
29(4):635657,
1989.
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G. A. Geist and E. G. Ng.
Task scheduling for parallel sparse Cholesky factorization.
International Journal of Parallel Programming,
18(4):291314,
1989.
Keyword(s): Parallel computing,
Cholesky factorization,
Task scheduling,
Subtreetosubcube mapping.
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A. George and J. W. H. Liu.
The evolution of the minimum degree ordering algorithm.
SIAM Review,
31(1):119,
1989.
Keyword(s): Sparse matrix ordering,
Minimum degree algorithm,
Computational complexity.
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A. George,
J. W. H. Liu,
and E. Ng.
Communication results for parallel sparse Cholesky factorization on a hypercube.
Parallel Computing,
10(3):287298,
1989.
Keyword(s): Parallel computing,
Cholesky factorization,
Task scheduling,
Subtreetosubcube mapping.
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J. W. H. Liu.
The minimum degree ordering with constraints.
SIAM Journal on Scientific and Statistical Computing,
10(6):11361145,
1989.
Keyword(s): Minimum degree ordering.
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I. S. Duff,
A. M. Erisman,
C. W. Gear,
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Sparsity structure and Gaussian elimination.
SIGNUM Newsletter,
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1988.
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J. R. Gilbert and T. Peierls.
Sparse partial pivoting in time proportional to arithmetic operations.
SIAM Journal on Scientific and Statistical Computing,
9(5):862874,
1988.
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J. W. H. Liu.
Equivalent sparse matrix reordering by elimination tree rotations.
SIAM Journal on Scientific and Statistical Computing,
9(3):424444,
1988.
Keyword(s): Multifrontal method,
Elimination tree,
Equivalent reordering,
Outofcore factorization,
Cholesky factorization.
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J. W. Ruge and K. Stüben.
Algebraic multigrid.
In S. F. McCormick, editor, Multigrid Methods,
chapter 4,
pages 73130.
SIAM,
Philadelphia, Pennsylvania,
1987.
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M. L. Fredman and R. E. Tarjan.
Fibonacci heaps and their uses in improved network optimization algorithms.
J. ACM,
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1987.
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J. R. Gilbert and R. E. Tarjan.
The analysis of a nested dissection algorithm.
Numerische Mathematik,
50(4):377404,
1987.
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I. S. Duff,
A. M. Erisman,
and J. K. Reid.
Direct Methods for Sparse Matrices.
Oxford University Press,
London,
1986.
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L. Lovasz and M. D. Plummer.
Matching Theory,
NorthHolland mathematics studies.
Elsevier Science Publishers,
Amsterdam, Netherlands,
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J. W. H. Liu.
A compact row storage scheme for Cholesky factors using elimination trees.
ACM Transactions on Mathematical Software,
12(2):127148,
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J. W. H. Liu.
On the storage requirement in the outofcore multifrontal method for sparse factorization.
ACM Transactions on Mathematical Software,
12(3):249264,
1986.
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M. Luby.
A simple parallel algorithm for the maximal independent set problem.
SIAM Journal on Computing,
15(4):10361053,
1986.
Keyword(s): Maximal independent set.
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J. W. H. Liu.
Modification of the minimumdegree algorithm by multiple elimination.
ACM Transactions on Mathematical Software,
11(2):141153,
1985.
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J. H. Reif.
Depthfirst search is inherently sequential.
Information Processing Letters,
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1985.
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H. D. Simon.
Incomplete LU preconditioners for conjugategradienttype iterative methods.
In Proceedings of the 1985 Reservoir Simulation Symposium,
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A. Pothen.
Sparse Null Bases and Marriage Theorems.
PhD thesis,
Department of Computer Science, Cornell University, Ithaca, New York,
1984.
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I. S. Duff and J. K. Reid.
The multifrontal solution of unsymmetric sets of linear equations.
SIAM Journal on Scientific and Statistical Computing,
5(3):633641,
1984.
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D. J. Rose.
Convergent regular splittings for singular $M$matrices.
SIAM Journal on Algebraic and Discrete Methods,
5(1):133144,
1984.
[bibtexkey = rose:84]

R. E. Tarjan.
Data Structures and Network Algorithms,
volume 44 of CBMSNSF Regional Conference Series in Applied Mathematics.
SIAM,
Philadelphia, PA, USA,
1983.
[bibtexkey = tarj:83]

I. S. Duff and J. K. Reid.
A note on the work involved in nofill sparse matrix factorization.
IMA Journal on Numerical Analysis,
1:3740,
1983.
[bibtexkey = dure:83b]

I. S. Duff and J. K. Reid.
The multifrontal solution of indefinite sparse symmetric linear equations.
ACM Transactions on Mathematical Software,
9:302325,
1983.
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S. C. Eisenstat,
M. C. Gursky,
M. H. Schultz,
and A. H. Sherman.
The Yale sparse matrix package I: The symmetric codes.
International Journal for Numerical Methods in Engineering,
18:11451151,
1982.
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J. A. G. Jess and H. G. M. Kees.
A data structure for parallel L/U decomposition.
IEEE Transactions on Computers,
31(3):231239,
1982.
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R. Schreiber.
A new implementation of sparse Gaussian elimination.
ACM Transactions on Mathematical Software,
8(3):256276,
1982.
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I. S. Duff.
Full matrix techniques in sparse Gaussian elimination.
In G. A. Watson, editor,
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C. M. Fiduccia and R. M. Mattheyses.
A lineartime heuristic for improving network partitions.
In DAC '82: Proceedings of the 19th Conference on Design Automation,
Piscataway, NJ, USA,
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1982.
IEEE Press.
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I. S. Duff and J. K. Reid.
MA27A set of Fortran subroutines for solving sparse symmetric sets of linear equations.
Technical report AERE R10533,
HMSO,
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1982.
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A. George and J. W. H. Liu.
Computer Solution of Large Sparse Positive Definite Systems.
PrenticeHall,
Englewood Cliffs, N.J.,
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I. S. Duff.
Algorithm 575: Permutations for a zerofree diagonal.
ACM Transactions on Mathematical Software,
7(3):387390,
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I. S. Duff.
On algorithms for obtaining a maximum transversal.
ACM Transactions on Mathematical Software,
7(3):315330,
1981.
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M. Yannakakis.
Computing the minimum fillin is NPcomplete.
SIAM Journal on Algebraic and Discrete Methods,
2(1):7779,
1981.
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A. George.
An automatic oneway dissection algorithm for irregular finite element problems.
SIAM Journal on Numerical Analysis,
17(6):740751,
1980.
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A. George and J. W. H. Liu.
A fast implementation of the minimum degree algorithm using quotient graphs.
ACM Transactions on Mathematical Software,
6(3):337358,
1980.
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A. George and J. W. H. Liu.
A minimal storage implementation of the minimum degree algorithm.
SIAM Journal on Numerical Analysis,
17(2):282299,
1980.
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J. R. Gilbert.
A note on the NPcompleteness of vertex elimination on directed graphs.
SIAM Journal on Algebraic and Discrete Methods,
1(3):292294,
1980.
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R. J. Lipton,
D. J. Rose,
and R. E. Tarjan.
Generalized nested dissection.
SIAM Journal on Numerical Analysis,
16(2):346358,
1979.
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R. J. Lipton and R. E. Tarjan.
A separator theorem for planar graphs.
SIAM Journal on Applied Mathematics,
36:177189,
1979.
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I. S. Duff and J. K. Reid.
Algorithm 529: Permutations to block triangular form.
ACM Transactions on Mathematical Software,
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I. S. Duff and J. K. Reid.
An implementation of Tarjan's algorithm for the block triangularization of a matrix.
ACM Transactions on Mathematical Software,
4(2):137147,
1978.
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A. George and J. W. H. Liu.
An automatic nested dissection algorithm for irregular finite element problems.
SIAM Journal on Numerical Analysis,
15(5):10531069,
1978.
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A. George and D. R. McIntyre.
On the application of the minimum degree algorithm to finite element systems.
SIAM Journal on Numerical Analysis,
15(1):90112,
1978.
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A. George,
W. G. Poole,
and R. G. Voigt.
Incomplete nested dissection for solving $n$ by $n$ grid problems.
SIAM Journal on Numerical Analysis,
15(4):662673,
1978.
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I. Gustafsson.
A class of first order factorization methods.
BIT Numerical Mathematics,
18(2):142156,
1978.
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D. J. Rose and R. E. Tarjan.
Algorithmic aspects of vertex elimination in directed graphs.
SIAM Journal on Applied Mathematics,
34(1):176197,
1978.
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B. Speelpenning.
The generalized element method.
Technical report UIUCDCSR78946,
Department of Computer Science, University of Illinois at UrbanaChampaign, Illinois,
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I. S. Duff.
On permutations to block triangular form.
Journal of the Institute of Mathematics and its Applications,
19(3):339342,
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J. A. Meijerink and H. A. van der Vorst.
An iterative solution method for linear systems of which the coefficient matrix is a symmetric $M$matrix.
Mathematics of Computation,
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F. G. Gustavson.
Finding the block lowertriangular form of a sparse matrix.
In J. R. Bunch and D. J. Rose, editors, Sparse Matrix Computations,
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Academic Press,
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I. S. Duff,
A. M. Erisman,
and J. K. Reid.
On George's nested dissection method.
SIAM Journal on Numerical Analysis,
13(5):686695,
1976.
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N. E. Gibbs,
W. G. Poole,
and P. K. Stockmeyer.
An algorithm for reducing the bandwidth and profile of a sparse matrix.
SIAM Journal on Numerical Analysis,
13(2):236250,
1976.
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W.H. Liu and A. H. Sherman.
Comparative analysis of the CuthillMcKee and the Reverse CuthillMcKee ordering algorithms for sparse matrices.
SIAM Journal on Numerical Analysis,
13(2):198213,
1976.
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D. J. Rose,
R. E. Tarjan,
and G. S. Lueker.
Algorithmic aspects of vertex elimination on graphs.
SIAM Journal on Computing,
5(2):266283,
1976.
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R. A. Willoughby.
A characterization of matrix irreducibility.
In L. Collatz,
G. Meinardus,
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volume 29 of International Series of Numerical Mathematics,
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Birkhäuser Verlag,
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A. George.
On block elimination for sparse linear systems.
SIAM Journal on Numerical Analysis,
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D. J. Rose and G. F. Whitten.
Automatic nested dissection.
In ACM 74: Proceedings of the 1974 annual conference,
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ACM.
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A. George.
Nested dissection of a regular finite element mesh.
SIAM Journal on Numerical Analysis,
10(2):345363,
1973.
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A. J. Hoffman,
M. S. Martin,
and D. J. Rose.
Complexity bounds for regular finite difference and finite element grids.
SIAM Journal on Numerical Analysis,
10(2):364369,
1973.
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J. E. Hopcroft and R. M. Karp.
An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs.
SIAM Journal on Computing,
2(4):225231,
1973.
Keyword(s): Matching.
[bibtexkey = hoka:73]

I. S. Duff.
Analysis of Sparse Systems.
PhD thesis,
Oxford University,
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1972.
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D. J. Rose.
A graphtheoretic study of the numerical solution of sparse positive definite systems of linear equations.
In R. C. Read, editor, Graph Theory and Computing,
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Academic Press,
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Keyword(s): Minimum degree algorithm.
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R. E. Tarjan.
Depthfirst search and linear graph algorithms.
SIAM Journal on Computing,
1(2):146160,
1972.
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A. J. George.
Computer Implementation of the Finite Element Method.
PhD thesis,
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Stanford, CA, USA,
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B. M. Irons.
A frontal solution program for finiteelement analysis.
International Journal for Numerical Methods in Engineering,
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B. W. Kernighan and S. Lin.
An efficient heuristic procedure for partitioning graphs.
The Bell System Technical Journal,
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D. J. Rose.
Triangulated graphs and the elimination process.
Journal of Mathematical Analysis and Applications,
32:597609,
1970.
Keyword(s): Elimination process,
Triangulated graph.
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E. Cuthill and J. McKee.
Reducing the bandwidth of sparse symmetric matrices.
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W. F. Tinney and J. W. Walker.
Direct solutions of sparse network equations by optimally ordered triangular factorization.
Proceedings of the IEEE,
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Keyword(s): Minimum degree algorithm.
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A. L. Dulmage and N. S. Mendelsohn.
Remarks on solutions of the optimal assignment problem.
SIAM Journal on Applied Mathematics,
11(4):11031109,
1963.
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A. L. Dulmage and N. S. Mendelsohn.
Two algorithms for bipartite graphs.
SIAM Journal on Applied Mathematics,
11(1):183194,
1963.
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S. Parter.
The use of linear graphs in Gauss elimination.
SIAM Review,
3(2):119130,
1961.
Keyword(s): Elimination process.
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A. L. Dulmage and N. S. Mendelsohn.
A structure theory of bipartite graphs of finite exterior dimension.
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1959.
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A. L. Dulmage and N. S. Mendelsohn.
Coverings of bipartite graphs.
Canadian Journal of Mathematics,
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1958.
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C. Berge.
Two theorems in graph theory.
Proceedings of the National Academy of Sciences of the USA,
43:842844,
1957.
Keyword(s): Matching,
Alternating path,
Augmenting path,
Vertex cover.
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H. M. Markowitz.
The elimination form of the inverse and its application to linear programming.
Management Science,
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1957.
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M. Hall, Jr..
An algorithm for distinct representatives.
The American Mathematical Monthly,
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H. W. Kuhn.
The Hungarian method for the assignment problem.
Naval Research Logistics Quarterly,
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[bibtexkey = kuhn:55]

P. Hall.
On representatives of subsets.
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1935.
[bibtexkey = hall:35]
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Last modified: Wed Jul 21 11:49:20 2010
Author: Bora Uçar.