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Nonexpansive matrices with applications to solutions of linear systems by fixed point iterations. (English) Zbl 1187.65031

Summary: We characterize (i) matrices which are nonexpansive with respect to some matrix norms, and (ii) matrices whose average iterates approach zero or are bounded. Then we apply these results to iterative solutions of a system of linear equations.

MSC:

65F10 Iterative numerical methods for linear systems
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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References:

[1] Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge, UK; 1985. · Zbl 0576.15001 · doi:10.1017/CBO9780511810817
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[4] Ishikawa S: Fixed points and iteration of a nonexpansive mapping in a Banach space.Proceedings of the American Mathematical Society 1976,59(1):65-71. 10.1090/S0002-9939-1976-0412909-X · Zbl 0352.47024 · doi:10.1090/S0002-9939-1976-0412909-X
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