Several New Methods For Judging Nonsingular H-matrices And Block H-matrices

Nonsingular (block) H -matrices is an special class of matrices with important role and application in many fields such as computational mathematics, mathematical physics, convergence of iterative methods, stability of control systems and so on. But in practice it is difficult to determine a matrix, especially for a large matrix, is an H -matrix or not. Under scholars abroad and home hard work there are many important results.In this paper, we study the methods for judging nonsingular (block) H -matrices by using the properties ofα-diagonally dominant matrices andα-chains diagonally dominant matrices, and applying some techniques in matrix theory and inequalities, which improve and extend the corresponding results recently , and give some numerical examples to illustrate our theory is effective.In chapter one, we introduce the meaning and studying actuality of (block) H -matrices, several definitions and symbols and the main work we have done are given.In chapter two, from two aspects, namely the whole and the partition, we obtain several new methods for judging nonsingular (block) H -matrices by using the properties ofα-chains diagonally dominant matrices, and applying some techniques in matrix theory and inequalities. At the same time, we give the corresponding determination conditions as the considered matrix is an irreducible matrix. These conditions have improved and generalized some existed results. Finally, we illustrate the effectiveness with numerical examples.In chapter three, on the basis of determining point H -matrices, we get some sufficient conditions for nonsingular H -matrices by applying block matrix technology, which improve and extend some corresponding results recently. Finally, we illustrate the effectiveness with numerical examples.