Some Methods For Judging Nonsingular H-matrix

Nonsingular H-matrix is an extremely important class of special matrices in matrix theory,which is in widespread application in many fields such as com-putational mathematics,mathematical physics,economics,biology,stability of control systems,and convergence of iterative methods and so on.In practice,it is rather difficult to determine whether a matrix(especially higher order ma,-trix)is an nonsingular H-matrix or not.Therefore,it is of great theoretical and practical value to study the methods for judging nonsingular H-matrix,and provide the concise and practical criteria,and construct fast and efficient iterative identification algorithms.This paper mainly studies the direct identification methods,the progressive identification methods and the iterative identification algorithm of nonsingular H-matrix.This paper is divided into four chapters,each of which reads as follows:In chapter one,we introduce the research background and significance of nonsingular H-matrix,the main work of paper,and the related symbols,defi-nitions,lemmas involved.In chapter two,the direct,criterion for nonsingular H-matrix is studied.According to definition and properties of the nonsingular H-matrix,we obtain several new criteria for nonsingular H-matrix by mean of constructing appro-priate coefficients,selecting new positively diagonal matrix factors and using the inequality techniques,and some recent results are improved.Finally,we verified the effectiveness of the results by numerical examples.In chapter three,the progressive criteria of nonsingular H-matrix has been researched.Using the properties of ?-chains diagonally dominant matrix,we obtain several new progressive criteria for nonsingular H-matrix by mean of se-lecting progressive coefficient,constructing new positively diagonal matrix fac-tors and using the inequality techniques,and some recent results are improved.Finally,we verified the validity of the results by numerical examples.In chapter four,we study the iterative decision algorithm of nonsingular H-matrix.In this chapter,a non-parameter iterative decision algorithm and a non-parameter interleaves iterative decision algorithm are presented respec-tively.For the non-parameter interleaved iterative identification algorithm,an irreducible matrix or not nonsingular H-matrix is given arbitrarily,the result can always be determined by finite number of iterations,and the algorithm pro-gram is written by Matlab software.The numerical example is used to illustrate the iteration of the related results.Fewer times and a wider range of judgments have improved recent results...