TY - JOUR
T1 - Complete stagnation of
JF - Linear Algebra and its Applications
Y1 - 2003
A1 - Zavorin, Ilya
A1 - O'Leary, Dianne P.
A1 - Elman, Howard
KW - Convergence
KW - GMRES
KW - iterative methods
KW - Stagnation
AB - We study problems for which the iterative method for solving linear systems of equations makes no progress in its initial iterations. Our tool for analysis is a nonlinear system of equations, the stagnation system, that characterizes this behavior. We focus on complete stagnation, for which there is no progress until the last iteration. We give necessary and sufficient conditions for complete stagnation of systems involving unitary matrices, and show that if a normal matrix completely stagnates then so does an entire family of nonnormal matrices with the same eigenvalues. Finally, we show that there are real matrices for which complete stagnation occurs for certain complex right-hand sides but not for real ones.
VL - 367
SN - 0024-3795
UR - http://www.sciencedirect.com/science/article/pii/S0024379502006122
M3 - 16/S0024-3795(02)00612-2
ER -