Criteria For Generalized Block Strictly Diagonally Dominant Matrix

In many fields such as computational mathematics, system engineering and control theory, matrix theory is an important tool. Generalized (block) strictly diagonally dominant matrix is an important special matrix, which plays an im-portant role in many areas such as numerical algebra, control systems and so on.In this paper, by using the properties ofα-(block)diagonally dominant matri-ces andα-chains (block) diagonally dominant matrices, applying some inequality techniques, we discuss the criteria of generalized block strictly diagonally dom-inant matrices, and give some numerical examples to illustrate the effectiveness of our results.In chapter one, we introduce the background of generalized block strictly di-agonally dominant matrices, several definitions and symbols and the main work of this paper.In chapter two, on the basis of determining point generalized strictly diag-onally dominant matrices, applying block matrix technology and the properties of matrix norm, constructing positively diagonal matrix, we get some sufficient conditions for generalized block strictly diagonally dominant matrix. Finally, we illustrate the effectiveness with numerical examples.In chapter three, we obtain several new methods for judging nonsingular generalized block strictly diagonally dominant matrices by using the properties of a-chains diagonally dominant matrices and some inequality techniques. At the same time, we give the corresponding determination conditions as the considered matrix is an irreducible matrix. Finally, we illustrate the effectiveness with nu-merical examples.In chapter four, by constructing positively diagonal factors, employing some inequality techniques of matrix norm and the properties of M matrix, we present another determination method for generalized block strictly diagonally dominant matrices by using the properties ofα-chains diagonally dominant matrices. The superiority of our new results is demonstrated by some numeric examples.