Abstract
We develop conditions under which a product Q1=0 Ti of matrices chosen from a possibly innite set of matricesS =fTjjj2 Jg converges. We obtain the following conditions which are sucient for the convergence of the product: There exists a vector norm such that all matrices in S are nonexpansive with respect to this norm and there exists a subsequencefikg 1=0 of the sequence of the nonnegative integers such that the corresponding sequence of operators Tik 1=0 converges to an operator which is paracontracting with respect to this norm. We deduce the continuity of the limit of the product of matrices as a function of the sequencesfikg1=0 . But more importantly, we apply our results to the question of the convergence of inner{outer iteration schemes for solving singular consistent linear systems of equations, where the outer splitting is regular and the inner splitting is weak regular.
Keywords
MathematicsMatrix normSequence (biology)Norm (philosophy)Limit of a sequenceInner product spaceConvergence (economics)Singular valueProduct (mathematics)Operator (biology)Infinite productPure mathematicsLimit (mathematics)Applied mathematicsMathematical analysisCombinatoricsEigenvalues and eigenvectors
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Publication Info
- Year
- 1994
- Type
- article
- Volume
- 2
- Pages
- 193
- Citations
- 46
- Access
- Closed
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Cite This
L. Elsner,
Rafael Bru,
Michael Neumann
(1994).
Convergence of infinite products of matrices and inner-outer iteration schemes.
Publikationen an der Universität Bielefeld (Universität Bielefeld)
, 2
, 193.