Several Determination Method Of Non-Singular H-Matrix

Non-singular H-matrix is an actual context of a broad category matrix, many problems often attributed to one or a number of large scale sparse matrix linear algebraic equations to solve, and we often assume the coefficient matrix is Non-singular H-matrix in the linear algebraic equations. At the same time, it plays an important role in computational mathematics, control theory, electric system, economy mathematics and many other fields. However, the practical discrimination of H-matrix is very difficult. So, it's meaningful to judge if a matrix is H-matrix or not. In recent years, many domestic and overseas scholars have been working on its properties and criterion, and have obtained lots of important results.This article, based on the research results, according to the definition of H-matrix, from the element of matrix itself, apply the properties of diagonally dominant matrices,α-diagonally dominant matrices andα-chain diagonally dominant matrices, and it selected a different positive diagonal matrix factors, used of a comprehensive selection of inequalities scaling techniques, finally, it got several simple and practical sufficient condition for non-singular H-matrix, improved and promoted the some research results.In chapter one,we introduced the background, application and the research status quo of H-matrices,and then gave a few symbol, definitions and lemma conventions.Chapter two mainly in two different subscript set (N1, N2)of matrix elements with different coefficients factor, which selected the positive diagonal matrix's diagonal factors, combined with the inequality scaling techniques, introduced new practical criterion, and come to irreducible matrix, nonzero elements chain matrix corresponding conclusions and numerical examples are proved for its effectiveness.Chapter three firstly extend the concept ofα-diagonally dominant matrix to generalizedα-diagonally dominant matrix, then construct some multiplier factors, and apply the concepts and properties ofα-diagonally dominant matrix, obtained some simple criterion for non-singular H-matrix, and then verify their effectiveness with numerical example.Chapter four given the related concepts ofα-chain diagonally dominant matrix, on the condition of strictlyα-chain diagonally dominant and the irreducibleα-chain diagonally dominant, structured an appropriate positive diagonal matrix D and combine of inequality-reduction techniques, so that AD is a strictly diagonal dominant matrix, and got the corresponding conclusion.