Japan Journal of Industrial and Applied Mathematics

, Volume 11, Issue 2, pp 289-342

First online:

Nonnegative splitting theory

  • Zbigniew I. WoźnickiAffiliated withInstitute of Atomic Energy

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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