Daniel B Szyld, Temple University
Event Date
2026-04-15
Event Time
04:00 pm ~ 05:00 pm
Event Location
617 Wachman Hall
We extend results known for the randomized (point and block)
Gauss-Seidel and the Gauss-Southwell methods
for the case of a Hermitian and positive definite matrix to certain classes of
non-Hermitian matrices. We consider cases with overlapping variables
(as in Domain Decomposition). We obtain convergence results for a whole range of
parameters describing the probabilities in the randomized method or the greedy choice strategy in the
Gauss-Southwell-type methods. We identify those choices which make our convergence bounds best
possible.
One result is that the best convergence bounds that we obtain for the
expected values in the randomized algorithm are as good as the best for the deterministic,
but more costly algorithms of Gauss-Southwell type.
We use these new results to show a provable convergence rate for asynchronous iterations.
(Joint work with Andreas Frommer, Wuppertal)