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2010•Unpublished venueRequires access

α-Chain Diagonally Dominant Matrix and Criterion for Nonsingular H-Matrix

Miao Chen

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Abstract

Let A=(aij)∈Cn×n,if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A) be right for i∈N={1,2,…,n},then A is called a chain diagonally dominant matrix.the concept was extended to generalized α-chain diagonally dominant matrix,and the concept generalized α-chain diagonally dominant matrix was applied to obtain some new criteria condition for a matrix to be a nonsingular H-matrix.The results obtained improve the known corresponding results.Finally,a numerical example was given for illustrating advantage of results.

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What this paper is about

Let A=(aij)∈Cn×n,if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A) be right for i∈N={1,2,…,n},then A is called a chain diagonally dominant matrix.the concept was extended to generalized α-chain diagonally dominant matrix,and the concept generalized α-chain diagonally dominant matrix was applied to obtain some new criteria condition for a matrix to be a nonsingular H-matrix.The results obtained improve the known corresponding results.Finally,a numerical example was given for illustrating advantage of results.

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Available abstract

Let A=(aij)∈Cn×n,if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A) be right for i∈N={1,2,…,n},then A is called a chain diagonally dominant matrix.the concept was extended to generalized α-chain diagonally dominant matrix,and the concept generalized α-chain diagonally dominant matrix was applied to obtain some new criteria condition for a matrix to be a nonsingular H-matrix.The results obtained improve the known corresponding results.Finally,a numerical example was given for illustrating advantage of results.

Key concepts: Diagonally dominant matrix, Invertible matrix, Mathematics, Matrix (chemical analysis), M-matrix, Pure mathematics, Chain (unit), Combinatorics

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