The Inverse And Determinant Computation Of Some Sparse Matrixes

Sparse matrix computation has attracted extensive researches in recent years because it can have a lot of applications in reality. It is acknowledged that periodic tri-diagonal matrix and arrow matrix in sparse matrixes have been widely applied in engineering calculation. Based on the structures of periodic tri-diagonal matrix and arrow matrix, this paper focuses on the arithmetic of the inverse and determinant of periodic tri-diagonal matrix and arrow matrix, and presents some new computational algorithms by using some methods of matrix decomposition.Firstly, it discusses the inverse of periodic tri-diagonal matrix on matrix structure of periodic tri-diagonal matrix. And some new computational algorithms are created by matrix LU decomposition, matrix recursion, blocking matrix and matrix reduction technique of the inverse of periodic tri-diagonal matrix on its structure, and then the feasibility and the effectiveness of these computational algorithms are verified by numerical examples in consideration of a simple algorithm of the determinant of periodic tri-diagonal matrix.Secondly, on the basis of the structure of arrow matrix, an algorithm of the inverse and determinant of arrow matrix is presented by using the matrix blocking. At the same time, the effectiveness and the feasibility are tested by numerical examples.