Subdivision Iterative Numerical Determination Methods For Nonsingular H-matrices

As a special matrix class in matrix research,the nonsingular H-matrix is often used in computational mathematics,applied mathematics,mathematical physics and other disciplines.It is a key problem how to determine whether a matrix is the nonsingular H-matrix in the field of matrix research.In this paper,the decision problem of the nonsingular H-matrix were explored and the new conditions of subdivision iteration of the nonsingular H-matrix were obtained.The subdivision iterative judgment algorithm and the subdivision interleaved iterative judgment algorithm of the nonsingular H-matrix were designed based on the improved conditions of subdivision iteration.The main contents of this paper are as follows:Firstly,the application background and research status of the nonsingular H-matrix were introduced.Besides,several basic symbols,definitions,properties and lemmas involved were given.Secondly,the subdivision iteration judgment criteria for the nonsingular Hmatrix was studied.By combining the subdivision of matrix element subscript set with the construction of iterative scaling coefficient,the scaling degree of non-iterative scaling coefficient was expanded,and a set of sufficient conditions for subdivision iteration judgment with wider judgment range were obtained.Furthermore,several numerical examples were calculated to verify the superiority of judgment sufficient conditions in this paper.Thirdly,the subdivision iteration judgment progressive new criteria for the nonsingular H-matrix was studied.By further subdividing the non-diagonally dominant line interval and constructing the cyclic iterative progressive reduction coefficient,the scaling degree of the positive diagonal coefficient was expanded to realize the simultaneous scaling of both sides of the decision inequality.What ’s more,a set of progressive conditions for subdivision iteration judgment were obtained.Similarly,several numerical examples were calculated to verify the superiority of progressive judgment conditions in this paper.Fourthly,the subdivision iteration judgment algorithm of the nonsingular H-matrix was studied.According to two sets of new criteria for judging nonsingular H-matrices proposed in this paper,two sets of subdivision iterative judgment algorithms without/with parameters were designed.By constructing the convergent iterative sequence of the judgment matrix and the progressive subdivision iterative judgment coefficient,the nonsingular H-matrix judgment algorithm with double iteration judgment was accomplished,which was more efficient than single iterative decision algorithm.Similarly,several numerical examples were calculated to verify the feasibility and high efficiency of the subdivision iteration judgment algorithm in this paper.Finally,the subdivision interleaved iterative judgment algorithm of the nonsingular H-matrix was studied based on the subdivision iteration judgment algorithm mentioned above in this paper.According to the parity of subdivision recursion times,the cyclic iteration judgment conditions in the algorithm are classified and crossed to construct different progressive judgment coefficients,so as to realize the double cyclic iteration judgment of odd-even interleaved determination,and the subdivision interleaved iteration judgment algorithm with fewer iterations was obtained.Similarly,several numerical examples were calculated to verify the high efficiency of the subdivision interleaved iterative judgment algorithm in this paper.