Matrix homographic iterations and bounds for the inverses of certain band matrices

Decay Rates for Inverses of Band Matrices

Spectral theory and classical approximation theory are used to give a new proof of the exponential decay of the entries of the inverse of band matrices. The rate of decay oí A'1 can be bounded in terms of the (essential) spectrum of A A* for general A and in terms of the (essential) spectrum of A for positive definite A. In the positive definite case the bound can be attained. These results are...

Bounds for Inverses of Triangular Toeplitz Matrices

This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...

Mosaic Ranks for the Inverses to Band Matrices

After reminding the de nition of mosaic ranks we estimate them from above for the inverses to band matrices The estimate grows logarithmically with the matrix size The result presented in this note should be compared with the well known descriptions of the inverses to band matrices as semisep arable matrices Our approach still excells in that it holds under much weaker assumptions Introduction ...

ℋ-matrix approximability of the inverses of FEM matrices

We study the question of approximability for the inverse of the FEM stiffness matrix for (scalar) second order elliptic boundary value problems by blockwise low rank matrices such as those given by the H-matrix format introduced by Hackbusch (Computing 62(2):89–108, 1999). We show that exponential convergence in the local block rank r can be achieved. We also show that exponentially accurate LU...

Some Observations on Inverses of Band Matrices and Low Rank Perturbations of Triangular Matrices