Nonnegative splitting theory Authors Zbigniew I. Woźnicki Institute of Atomic Energy 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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