My name is Philippe Théveny. I am currently a PhD student in the ARIC team under the supervision of Nathalie REVOL.
My work focuses on the trade-off between efficiency and numerical quality of floating-point interval algorithms when implemented on multi-core processors.
Numerical computations with intervals provides a means to certify computed results but requires care in actual implementation to ensure both validity and tightness of the outcome.
In the particular case of linear algebra, interval arithmetic changes the operational constraints compared to usual numerical linear algebra:
In order to explicit these constraints and a solution that satisfy them while still being efficient and scalable, I am analyzing matrix-matrix multiplication and QR factorization as case studies.
I made some contributions to the following libraries of mathematical functions for floating-point numbers in arbitrary precision:
Conventional wisdom is not enough, vendors' public data are not enough, and benchmark analyses are perishable as hardware/software technology evolves. But openly available benchmark codes permit to understand, criticize, and reproduce measures and analyses for upgrade or update. Here are mine.
Benchmark details (pdf), reproduce it on your platform (binary128_emu-0.1.tar.gz )
JDEV2013.tar.gz Logistic map and its fixed points with interval Newton algorithm in arbitrary precision
eprcn.tar.gz Logistic map and interval Newton algorithm