The Inverse of Banded Matrices
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS
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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 5, 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.
- Theoretical Mathematics