The Properties Of α-diagonally Dominant Matrices And The Determination Of Generalized Strictly Diagonally Dominant Matrices

Generalized strictly diagonally dominant matrix play an important role in numerical algebra ,control theory ,electric system,economic mathematics and elastic dynamics and so on. But it isn't easy to determine whether the matrix is or not generalized strictly diagonally dominant matrix in reality, especially for the large matrices. Under scholar abroad and home hard work there are many important fruits. In this paper we obtain some new determination conditions from three aspects according to some exists theory and the property of αdiagonally dominant matrix, improve the determination conditions and give some numerical example to show our theory is effective. In chapter one, firstly, we introduce the properties of αdiagonally dominant matrix and some exists determination conditions of generalized strictly diagonally dominant matrix, then we give some new results for the criteria of generalized strictly diagonally dominant matrix, finally, we show the validity of these conclusions. In chapter two, by using the elements of the matrix we first construct some multiplier factors, then, use the properties of αdiagonally dominant matrix and the techniques of inequalities, we give some new determination conditions for generalized strictly diagonally dominant matrix, these theory have improved some existing results. In chapter three, at first we introduces two kinds locally double αdiagonally dominant matrix from the concept of αdiagonally dominant matrix, by using this conception and the properties of αdiagonally dominant matrix and the techniques of inequalities, we discuss the relation of locally double αdiagonally dominant matrix and generalized strictly diagonally dominant matrix, according to these relations we obtain some effective criteria for generalized strictly diagonally dominant matrix.