Exact Linear Algebra
ISSAC'07 Tutorial
"Some Recent Progress in Exact Linear Algebra and Related Questions"
Sunday July 29 16:00-18:30, 2007, University of Waterloo, Ontario,
Canada
Abstract:
We describe some major recent progress
in exact and symbolic linear algebra. These advances concern the improvement of
complexity estimates for fundamental problems
such as linear system solution, determinant, inversion and computation
of canonical forms. The matrices are over a
finite field, the integers, or univariate polynomials.
We show how selected techniques are key ingredients for
the new solutions: randomization and
algebraic conditioning,
lifting,
subspace approach, divide-double and conquer,
minimum matrix polynomial, matrix approximants.
These algorithmic progress allow the design of new generation
high performance libraries such as LinBox, and open various
research directions.
Extended abstract and bibliography:
pdf.
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