Inverse of Banded Matrices.

摘要

The inverses of r-banded matrices, for r = 1, 2, 3 have been thoroughly investigated as one can see from the references we provide. Let Br,n (1 less than or equal to r less than or equal to n) be an n x n matrix of entries (ai sub j), -r less than or equal to r, 1 less than or equal to j less than or equal to r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999), we give the LU factorization and the inverse of the matrix Br,n (if it exists). Our results are valid for an arbitrary square matrix (taking r = n), and so, we will give a new approach for computing the inverse of an invertible square matrix. Our method is based on Hessenberg submatrices associated to Br,n.