Nonnegative splitting theory Article

Received: 06 February 1992 Revised: 12 April 1993 DOI :
10.1007/BF03167226

Cite this article as: Woźnicki, Z.I. Japan J. Indust. Appl. Math. (1994) 11: 289. doi:10.1007/BF03167226
Abstract In this paper the nonnegative splitting theory, playing a fundamental role in the convergence analysis of iterative methods for solving large linear equation systems with monotone matrices and representing a broad class of physical and engineering problems, is formulated. As the main result of this theory, it is possible to make the comparison of spectral radii of iteration matrices in particular iterative methods.

Key words linear equation systems iterative methods monotone matrices eigenvalues eigenvectors regular nonnegative weak nonnegative and weak splittings comparison theorems Dedicated to my teacher and friend Professor Janusz R. Mika

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Authors and Affiliations 1. Institute of Atomic Energy Otwock-Swierk Poland