2011 Apr 09 at 09:30
DC 1302
Clément Pernet, Université Joseph Fourier
Gaussian elimination and the computation of the numerous related matrix factorizations are a key component in the design of high performance mathematical computation software. This talk is about a collection of algorithmic and implementation techniques that we found of prime importance when dealing with these computations in computer algebra. After setting algorithmic relations between most common gaussian elimination based matrix factorizations and normal forms, we will propose a set of reductions of all these computations to a universal matrix factorization, justified by time and space complexity analysis. We will then approach some aspects of dedicated implementations over GF(2) and the parallelization of gaussian elimination, showing in particular advantages over numerical linear algebra.
This talk is part of the East Coast Computer Algebra Day (ECCAD 2011). ECCAD is open to all and free to attend, but we encourage registration. See http://www.cs.uwaterloo.ca/conferences/eccad2011