Lim, Teck-Cheong Nonexpansive matrices with applications to solutions of linear systems by fixed point iterations. (English) Zbl 1187.65031 Fixed Point Theory Appl. 2010, Article ID 821928, 13 p. (2010). 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. Cited in 4 Documents MSC: 65F10 Iterative numerical methods for linear systems 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory Keywords:nonexpansive matrices; fixed point iterations; matrix norms; system of linear equations PDFBibTeX XMLCite \textit{T.-C. Lim}, Fixed Point Theory Appl. 2010, Article ID 821928, 13 p. (2010; Zbl 1187.65031) Full Text: DOI EuDML References: [1] Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge, UK; 1985. · Zbl 0576.15001 · doi:10.1017/CBO9780511810817 [2] Dunford N, Schwartz JT: Linear Operators, Part I. Interscience Publishers, New York, NY, USA; 1957. · Zbl 0128.34803 [3] Kincaid D, Cheney W: Numerical Analysis. Brooks/Cole, Pacific Grove, Calif, USA; 1991. · Zbl 0745.65001 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.