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2011•Unpublished venueRequires access

A Necessary and Sufficient Condition of α-Chain Strictly Diagonally Dominant Matrices

Xiaoying Zhao

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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 an α-chain diagonally dominant matrix.It gave an equivalent condition for chain strictly diagonally dominant matrices,and obtains a necessary condition for a matrix to be a nonsingular H-matrix indirectly.The result obtained improves the known corresponding results.At last,some numerical examples are given for illustrating advantages of the result.

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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 an α-chain diagonally dominant matrix.It gave an equivalent condition for chain strictly diagonally dominant matrices,and obtains a necessary condition for a matrix to be a nonsingular H-matrix indirectly.The result obtained improves the known corresponding results.At last,some numerical examples are given for illustrating advantages of the result.

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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 an α-chain diagonally dominant matrix.It gave an equivalent condition for chain strictly diagonally dominant matrices,and obtains a necessary condition for a matrix to be a nonsingular H-matrix indirectly.The result obtained improves the known corresponding results.At last,some numerical examples are given for illustrating advantages of the result.

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

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