Numerical Determination Methods For Nonsingular H-matrices

The H-matrix is a special class of matrices active in matrix theory,compu-tational mathematics,neural networks and cybernetics.It plays an important role in the application of theory,but in practical applications,how to distinguish the H-matrix is difficult.Therefore,it is important to study the nonsingular H-matrix simple and practical method to construct an efficient and stable iterative criteria algorithm,which has important theoretical and practical value.This paper mainly studies the direct criterion of H-matrix,progressive criteria condition,iterative criterion algorithms and interleaved iterative algo-rithm,and improves some recent results.The main contents are as follows:Firstly,we introduce the research background of the problems of judging nonsingular H-matrices,as well as several definitions,notations and the main work of this paper.Secondly,the direct criterion for nonsingular H-matrix is studied.Ac-cording to the definitions and properties of the nonsingular H-matrices,a new positively diagonal matrix transformation factor is constructed,and a new di-rect criteria condition is obtained by using the inequality scaling technique.Finally several numerical examples are presented to illustrate the improvement of existing results.Thirdly,the progressive criterion of nonsingular H-matrix is studied.We obtain a series of new progressive criteria conditions of nonsingular H-matrices by mean of constructing new positively diagonal matrix transformation factors and iterative construction methods.The new conditions of H-matrices improve some recent results,and numerical examples are used to verify the superiority of the new conditions.Fourthly,the iterative criterion algorithm of nonsingular H-matrix is stud-ied.we provide two sets of new iterative criterion algorithms with or without parameters by selecting positively diagonal matrix factors and parameters pro-gressively.The new algorithms are realized by Matlab language programming.Numerical simulation results are presented to verify that the new iterative al-gorithm is more efficient,the judgment range is wider.Some related results are improved.Lastly,the interleaved iterative algorithm of nonsingular H-matrix is stud-ied.In order to realize the idea of interleaved iteration,starting from a certain step of the algorithm,the process is divided into two sub-blocks,and when the parity check is met,one of the sub-blocks is selected.A new algorithm for parameterized interleaved iterative criterion of H-matrix is given to avoid that the matrix is a reducible matrix resulting the iterative process does not stop by introducing a parameter.For any given nonsingular H-matrix,the result can always be judged by finite step iteration.Finally,numerical examples are used to verify that the new algorithms are more efficient.