Several Criteria For Nonsingular H-matrices

Nonsingular H-matrices play important roles not only in pure mathematics, but also in many practical sciences. Since the theory of nonsingular H-matrices was established in20century, its study has been being considerably active. In recent years, many scholars in the world have paid their attention on this theory, they have established several criteria for nonsingular H-matrices, and have obtained some important and classical results. In practice, solutions of many problems can be summarized up to identify that the coefficient matrices are nonsingular H-matrices. Therefore, it is significant to look for numerical methods of judging nonsingular H-matrices and to provide effective and practical criteria.In this paper, by applying the method of subdivided region and iteration, geometrically α-bidiagonally dominant, and α-local doubly diagonally dominant, we present several types of practical criteria for identifying nonsingular H-matrices, which improve some related results, the effectiveness and advantages of the presented criteria are demonstrated by numerical examples.The thesis is divided into four chapters.In Chapter1, we introduce the background of judging nonsingular H-matrices, as well as the developing situation, the present situation, and the main conclusions of this thesis.In Chapter2, by applying the method of subdivided region and iteration, we obtain several class of practical criteria for judging nonsingular H-matrices, which improve some existing related results.In Chapter3, according to the theory of geometrically α-bidiagonally dominant, we establish several necessary and sufficient conditions for identifying strictly geometrically α-bidiagonally dominant matrices. Furthermore, we give several practical criteria of nonsingular H-matrices, which improve the recent results effectively.In Chapter4, by defining and studying a type of α-local doubly diagonally dominant matrices, we establish several new practical criteria for identifying nonsingular H-matrices. As a results, the theory of the criteria for nonsingular H-matrices is well expanded.Numerical examples are given in each Chapter to illustrate their practicability.