Richardson method and totally nonnegative linear systems

We show that modified Richardson method converges for any nonsingular totally nonnegative stochastic matrix for any choice of the parameter between 0 and 2. We present a variant of the modified Richardson method that is convergent for any nonsingular totally nonnegative matrix. We obtain the optimal...

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Bibliographic Details
Published in:Linear algebra and its applications 2010-12, Vol.433 (11), p.2010-2017
Main Authors: Carnicer, J.M., Delgado, J., Peña, J.M.
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Richardson method
Sciences and techniques of general use
Stochastic matrices
Totally nonnegative matrices
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Summary:We show that modified Richardson method converges for any nonsingular totally nonnegative stochastic matrix for any choice of the parameter between 0 and 2. We present a variant of the modified Richardson method that is convergent for any nonsingular totally nonnegative matrix. We obtain the optimal parameter value for this method and give a procedure for estimating it. Numerical experiments are presented.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2010.07.007