Drazin Inverse Of Special Block Matrix And The Missing Items Vandermonde Matrix Inverse

With the fast development of computer science, it presents a lot of large or super-large calculation problems in many fields of military technologies and the construction of nation's economy. For those problems, their matrices often have some special structure. So it is meaningful to decrease the numerical measure of matrices computation by utilizing their special structure and taking some skillful methods.The algorithm to solve the inverse of a matrix is a more active branch in matrix theory. In this paper, the Drazin inverses of singular matrices are considered. If A is a singular matrix and satisfies some conditions, the Drazin inverse of A is given, and it can be expressed explicitly by elements of A. In particular, the fast algorithms are given for tridiagonal Toeplitz matrices and tridiagonal matrices by using this result. The inverses of a class of Vandermonde-like matrices are also considered. And we deduced the fast algorithm for computing the inverse of Vandermonde-like matrix using 0(n2) operations.