2011•Journal of Sichuan Normal UniversityRequires access

New Sufficient Conditions for Nonsingular H-matrices

Tian Qiu-ju

Abstract

In the theory and applications of numerical linear algebra,the class of H-matrices is very important.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,then A is called an α-chain diagonally dominant matrix.In this paper,the concept is extended to that of generalized α-chain diagonally dominant matrices.By using the properties of α-chain diagonally dominant matrices and applying some techniques of inequalities,some new sufficient conditions for a matrix to be a nonsingular H-matrix are obtained.The results obtained improve the known corresponding results.At last a numerical example is given for illustrating the advantage of our results.

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Key concepts: Diagonally dominant matrix, Invertible matrix, Mathematics, Matrix (chemical analysis), Chain (unit), Pure mathematics, Algebra over a field, Class (philosophy)