Some Discrimination Methods Of H-matrix And Generalized H-matrices

Matrix theories are widely used in statistics, economics, engineering technologyand other felds in recent years. The H-matrix and generalized H-matrix, as thespecial matrix, has important theoretical value and practical signifcance in numer-ical algebra and matrix analysis.In this paper, applying the relevant properties of strictly γ-diagonally domi-nant matrix, we present several new sufcient conditions of H-matrix; by utilizingthe equivalent condition of M-matrix and generalized M-matrix, we obtain severalnew criterion theorems of generalized H-matrix.In chapter one, we frst introduce some theoretical background, applicationbackground knowledge and recent research for H-matrix and generalized H-matrix.What’s more, our main works, some basic symbols and defnitions are given in ourpaper.In chapter two, by applying the relevant properties of strictly γ-diagonally dom-inant matrix, combining with H o¨lder inequalities and other relevant techniques ofinequalities, we get several new sufcient conditions of H-matrix. Further, splittingthe index set by the analysis of the characteristics of the matrix elements, bindingmethod of determining, another determination method to be H-matrices is also ob-tained. The conditions are efectiveness by some numerical examples.In chapter three, by utilizing the equivalent condition of M-matrix and gener-alized M-matrix, analyzing the feature of block matrix and contracting correlativespecial matrix, we obtain one new criterion theorem of generalized H-matrix. Fur-ther, by combing with matrix’ Hadamard product and its relevant inequalities, thematrix’ estimate of spectral radius methods etc., other new sufcient conditions ofgeneralized H-matrix are obtained. The specifc numerical examples are given toillustrate the superiority of the results.