An Optimized Iterative Method for Numerical Solution of Large Systems of Equations Based on the Extremal Property of Zeroes of Chebyshev Polynomials

Authors:
O. M. Podvigina;V. A. Zheligovsky
Affiliations:
podvigina_o@maths.su.oz.au. School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia;zheligo_v@maths.su.oz.au
Venue:
Journal of Scientific Computing
Year:
1997

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Abstract

An iterative method suitable for numerical solution of large systems of equations is presented. An extremal property of the Chebyshev polynomials is established, providing a logical foundation for the proposed procedure. A modification of the method is applicable for evaluation of the maximal eigenvalue of a matrix with real eigenvalues and of the associated eigenvector.