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Subdivided and Iterative Criteria for Nonsingular H-Matrices

Quan Lu

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Abstract

Nonsingular H-matrices play an important role in matrix theory,economical mathematics,physics and power system theory,and so on,it is very necessary to know whether a matrix is a nonsingular H-matrix or not.In this paper,by utilizing the properties of generalized strictly α-diagonally dominant matrices and the relations between generalized strictly α-diagonally dominant matrices and nonsingular H-matrices,some subdivided and iterative criteria for nonsingular H-matrices are given by selecting coeffcient progressively and subdivided region,which extend and improve some related results.Effectiveness of these criteria is illustrated by numerical examples.

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What this paper is about

Nonsingular H-matrices play an important role in matrix theory,economical mathematics,physics and power system theory,and so on,it is very necessary to know whether a matrix is a nonsingular H-matrix or not.In this paper,by utilizing the properties of generalized strictly α-diagonally dominant matrices and the relations between generalized strictly α-diagonally dominant matrices and nonsingular H-matrices,some subdivided and iterative criteria for nonsingular H-matrices are given by selecting coeffcient progressively and subdivided region,which extend and improve some related results.Effectiveness of these criteria is illustrated by numerical examples.

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Available abstract

Nonsingular H-matrices play an important role in matrix theory,economical mathematics,physics and power system theory,and so on,it is very necessary to know whether a matrix is a nonsingular H-matrix or not.In this paper,by utilizing the properties of generalized strictly α-diagonally dominant matrices and the relations between generalized strictly α-diagonally dominant matrices and nonsingular H-matrices,some subdivided and iterative criteria for nonsingular H-matrices are given by selecting coeffcient progressively and subdivided region,which extend and improve some related results.Effectiveness of these criteria is illustrated by numerical examples.

Key concepts: Invertible matrix, Diagonally dominant matrix, Mathematics, Matrix (chemical analysis), Pure mathematics, Algebra over a field, Diagonal, Geometry

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