Several Types Of Criteria For Identifying Generalized Strictly Diagonally Dominant Matrices

Generalized strictly diagonally dominant matrix plays an important role in matrix theory and real applications. It has numerous applications in numerical algebra, cybernetics theory, electrical system theory, mathematics of economics, statistics and so on. Many scholars abroad and home have obtained lots of criteria for identifying generalized strictly diagonally dominant matrix by using iterative arithmetic and techniques in matrix theory and inequalities, and studied its properties and applications. By looking for positive diagonal matrix factors, we present several types of practical criteria for identifying generalized strictly diagonally dominant matrix, improve and extend some existing results. In chapter one, by looking at two types of rows, the strictly diagonally dominant rows( N₂) and the others( N₁ ), inspired by some existing criteria and by looking for positive diagonal matrix factors, we present a new simple criterion and prove it . We also can give new proofs for some existing criteria. In chapter two, we divide non-strictly diagonally dominant rows( N₁ ) into N₁¹ and N₁². By using the properties of part matrix elements in N1 , and by looking for positive diagonal matrix factors, we present some new sufficient conditions of generalized strictly diagonally dominant matrix and improve the recent results. In chapter three, we divide the rows of matrix into types finer than those in chapter one. Again by looking for positive diagonal matrix factors, we obtain several new criteria for identifying generalized strictly diagonally dominant matrix, improving some existing criteria. In chapter four, by defining and studying a type of local doublediagonally dominant matrix, we give some new criteria foridentifying generalized strictly diagonally dominant matrix, andextend some existing results. Numerical examples are given in each chapter to illustrate theirpracticability...