A generalized nonlinear diagonal dominance

Authors:
Ting-Zhu Huang;Yu-Bo Yuan
Affiliations:
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu Sichuan, China, P.R. China;School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu Sichuan, China, P.R. China
Venue:
International Journal of Computer Mathematics
Year:
2008

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A concept of nonlinear block diagonal dominance

Journal of Computational and Applied Mathematics
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables

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Abstract

The concept of strictly β-diagonally dominant matrices is introduced. This concept is directly related to solving a system of equations. In the linear case, the strictly β -diagonally dominant matrices contain the strictly diagonally dominant matrices. However, for systems of nonlinear equations, it is a challenge to present a better condition to make sure that the iteration algorithm used to solve them is convergent. A new class of nonlinear mappings and some properties are offered; moreover, the corresponding convergence theorems of the nonlinear Gauss-Seidel and Jacobi iterations are presented.