Some Methods For Judging Nonsingular H-matrix

Nonsingular H-matrix is a relatively active research in computational mathematics,mathematical physics,control theory and matrix theory.It is widely used in many subjects such as economics,biology,dynamical system theory and intelligence science and so on.However,it is difficult to determine whether a matrix is an H-matrix or not in normal practice.Therefore,it has great theoretical and practical value to study the determination methods of the H-matrix,to provide the concise and practical criteria and to construct fast and efficient iterative identification algorithms.In this paper,the direct criteria of the H-matrix,the progressive criteria and the interleaved iteration identification algorithm will be discussed.Some recent results have been improved.The main contents are as follows:Firstly,we introduced some background knowledge of H-matrix,including the meaning and recent works of the topic,we presented the summary of this paper,and several basic symbols,definitions,lemmas as well.Secondly,we researched the direct criteria of H-matrix.By using definition and properties of the nonsingular H-matrices,we obtained a series of new direct criteria for nonsingular H-matrices.By adding a new coefficient to construct the positive diagonal matrix transformation factor and inequality techniques,some recent results have been improved.Several numerical examples are given to show the advantages of this methods.Thirdly,the progressive criteria of H-matrix has been researched.By constructing positively diagonal factors progressively,some new progressive criteria for H-matrix have been obtained.Several numerical examples are given to prove the superiority of this new criteria.Obviously,the new progressive criterion is better than before,more widely used the previous results could be improved.Lastly,we researched the interleaved iteration identification algorithm of H-matrix.It provided a new type non-parameters interleaved iteration identification algorithm which can determine whether an irreducible matrix is an H-matrix or not with Limited iteration.Some numerical examples show that this algorithm is better than the previous algorithms,less iterative times,more widely used.And for a given matrix that is not an H-matrix,the algorithm can also judge faster.The previous results could be improved.