| The nonsingular H-matrix has very important practical value in the application of matrix theory,and the solution of many practical problems can be attributed to the problem of judging whether a matrix is the Hmatrix.In fact,it is difficult to study whether a matrix is nonsingular H-matrix,many scholars have done a lot of research and have obtained many results,but it is far from enough to solve many practical problems.Therefore,It is meaningful to get the simple and practical criterion of H-matrix.The main contents are as follows:Firstly,This paper introduces some background knowledge about nonsingular H-matrix,and gives the basic definitions,symbols and lemmas involved in the content of the paper.Secondly,the direct criterion of nonsingular H-matrix is studied.By analyzing the definition and properties of the H-matrix,the positively diagonal factors are selected,then the positively diagonal matrix is constructed,and a series of criteria for the H-matrix are given by using some techniques of the inequality.The paper proves the feasibility of the given criterion,and uses numerical examples to verify that the obtained results expand the judgment range of the H-matrix.Thirdly,the progressive method of nonsingular H-matrix is studied.By analyzing the properties of α-chain diagonally dominant matrix to select positively diagonal factors,and construct progressive coefficients that need to be improved,then give some new progressive methods for judging H-matrix.The progressive methods reduce calculation steps and improve the existing results in recent literature.Lastly,this paper researches the iterative algorithm of nonsingular Hmatrix.On the basis of the existing algorithm,the positively diagonal matrix factor is improved,and the iterative algorithm for the H-matrix is given.The improved algorithm reduces the number of iterations.At the same time,the convergence of the new iterative algorithm is proved,and it can always stop and draw conclusions after a finite number of iterations. |
