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New Criteria for Nonsingular H-matrices

Ru Jiang

Open publisher page 4 citations

Abstract

Nonsingular H-matrices play an important role in the research of matrix analysis and numerical algebra.Based on the concepts and properties of α-diagonally dominant matrices,irreducible α-diagonally dominant matrices and α-diagonally dominant matrices with a nonzero elements chain,two new criteria for nonsingular H-matrices are obtained firstly in this paper according to the partition of the row indices.Secondly,a more practical criterion is also obtained by applying the above results to the sum of the comparison matrix and its transpose.A numerical example is presented to illustrate the effectiveness of the presented criteria.

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What this paper is about

Nonsingular H-matrices play an important role in the research of matrix analysis and numerical algebra.Based on the concepts and properties of α-diagonally dominant matrices,irreducible α-diagonally dominant matrices and α-diagonally dominant matrices with a nonzero elements chain,two new criteria for nonsingular H-matrices are obtained firstly in this paper according to the partition of the row indices.Secondly,a more practical criterion is also obtained by applying the above results to the sum of the comparison matrix and its transpose.A numerical example is presented to illustrate the effectiveness of the presented criteria.

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Available abstract

Nonsingular H-matrices play an important role in the research of matrix analysis and numerical algebra.Based on the concepts and properties of α-diagonally dominant matrices,irreducible α-diagonally dominant matrices and α-diagonally dominant matrices with a nonzero elements chain,two new criteria for nonsingular H-matrices are obtained firstly in this paper according to the partition of the row indices.Secondly,a more practical criterion is also obtained by applying the above results to the sum of the comparison matrix and its transpose.A numerical example is presented to illustrate the effectiveness of the presented criteria.

Key concepts: Diagonally dominant matrix, Mathematics, Invertible matrix, Transpose, Partition (number theory), Matrix (chemical analysis), Algebra over a field, Diagonal

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