Theses and Dissertations
Date of Award
12-2022
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
First Advisor
Dr. Josef Sifuentes
Second Advisor
Dr. Cristina Villalobos
Third Advisor
Dr. Andras Balogh
Abstract
GMRES is an iterative method for solving linear systems that minimizes the residual over the k-dimensional Krylov subspace at iteration k. Murphy, Golub and Wathen in [11] show that saddle point type matrices can be preconditioned so that GMRES converges in two or three steps. Ipsen in [10] extends this work to matrixes where the (2,2) block is nonzero. However, the three step convergence result no longer holds in this case. In this thesis we investigate how many more steps are needed for convergence as a function of the size of that (2,2) block.
Recommended Citation
Mascorro, Miguel A., "GMRES Convergence of Block Preconditioners for Nonsymmetric Matrices" (2022). Theses and Dissertations. 1163.
https://scholarworks.utrgv.edu/etd/1163
Comments
Copyright 2022 Miguel A. Mascorro. All Rights Reserved.
https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/gmres-convergence-block-preconditioners/docview/2802169007/se-2?accountid=7119