Several Determination Method Study Of Non-Singular H-Matrix

Non-singular H-matrix has an important practical value and significance in computational mathematics, numerical algebra, control theory, economy mathematics and many other areas, which has taken widely attention from scholars at home and abroad, and done a lot of important work, This article would do further discussion to its nature, determination, application, and got the corresponding number of conclusions.This artical, based on the nature ofα-diagonally dominant matrices, partial double-diagonally dominant matrix , and it selected a different positive diagonal matrix factors and used of a comprehensive selection of inequalities scaling techniques, Finally, It got several non-singular matrix Criterion, improved and promoted the some recent research results and numerical examples are compared.Chapter One Firstly, The paper introduces the background, application and the research status quo of several special matrices, and then briefly introduced the main other chapters, finally gives a few definitions and symbol conventions.Chapter Two Under the the division of set N = N 1⊕N 2⊕N3, and in three different subscript set of matrix elements with different coefficients factor, which selected the positive diagonal matrix's diagonal factors, combined with the inequality scaling techniques, introducted a new practical criterion, but also come to irreducible matrix, nonzero elements chain matrix corresponding conclusions and numerical examples are proved for its effectiveness.Chapter Three by means of some methods in matrix theory and inequality of scaling techniques, constructing the corresponding positive diagonal matrix, obtained two simple determinaiton methods about certain types of non-singular H-matrix, and then verify their effectiveness with numerical examples.Chapter Four Given the related concepts on local (α,β)?double diagonally dominant matrices, on the condition of strictly local (α,β)?double diagonally dominant and the irreducible local (α,β)?double diagonally dominant matrices structured an appropriate positive diagonal matrix, obtained two practical criterion of non-singular H-Matrix.