Abstract

We examine the the convergence behavior of block GMRES and block FOM
and characterize the phenomenon of stagnation in block GMRES. Stagnation
is then related to the behavior of the block FOM method. As in previous
work, we generalize the block FOM method to generate well-defined
approximations in the case that block FOM would normally break down,
and these generalized solutions are used in our analysis. Two toy
numerical examples are given to illustrate what we have proven and
we also apply both block methods to a small application problem to
demonstrate the validity of the analysis in non-pathological cases.

Links

• http://arxiv.org/abs/1411.7801

BibTeX (Download)

@article{S.2014-3,
title = {Stagnation of block GMRES and its relationship to block FOM},
author = {Kirk M. Soodhalter},
url = {http://arxiv.org/abs/1411.7801},
year  = {2017},
date = {2017-01-01},
urldate = {2017-01-01},
journal = {Electronic Transactions on Numerical Analysis},
volume = {46},
pages = {162\textendash189},
abstract = {We examine the the convergence behavior of block GMRES and block FOM 
	and characterize the phenomenon of stagnation in block GMRES. Stagnation 
	is then related to the behavior of the block FOM method. As in previous 
	work, we generalize the block FOM method to generate well-defined 
	approximations in the case that block FOM would normally break down, 
	and these generalized solutions are used in our analysis. Two toy 
	numerical examples are given to illustrate what we have proven and 
	we also apply both block methods to a small application problem to 
	demonstrate the validity of the analysis in non-pathological cases.},
keywords = {published},
pubstate = {published},
tppubtype = {article}
}