The Study On Some Properties Of α-Nekrasov Matrix

Nekrasov matrix is a class of special matrices which has theoretical valuep and practical application background. Its distinct structure makes Nekrasov matrix has many nice properties and play a signi?cant role in numerical algebra,control theory, electrical power system theory, economical mathematics, statistics etc. In this paper, we propose several new subclasses of nonsingular H- matrix on the basis of the distinct structure of Nekrasov matrix, then we discuss the properties of α-Nekrasov matrix, product α-Nekrasov matrix, and S-α Nekrasov matrix,at last we give some new criterion of nonsingular H-matrix on the basis of our new matrix classes.In chapter one, we ?rst introduce background knowledge and recent research for results nonsingular H-matrix; and introduce our main works, some basic symbols and de?nitions.In chapter two, we propose the notation of α-Nekrasov matrix and S-α-Nekrasov matrix, then show both of them are the subclasses of Nonsingular Hmatrix. By using the methods of partitioning index set, according to some techniques of inequalities and the structure of α-Nekrasov matrix, we obtain several new criteria for non-singular H-matrices. These criteria for non-singular Hmatrices we obtain improve and extend some existing results. The e?ectiveness and excellence of these criteria are illustrated by numerical examples.In chapter three, we give a new matrix class Product α-Nekrasov matrix,which is also subclass of nonsingualr H-matrix. On the basis of the structure of Nekrasov matrix, using dividing index set twice and some techniques of inequalities, we obtain some new criteria for nonsingular H-matrices. A numerical example is used to show the e?ectiveness of our results.