Left inverses of matrices with polynomial decay

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...

Finding left inverses for operators on l(Z) with polynomial decay

We study the left-invertibility of infinite matrices indexed by metric spaces with polynomial growth. Under different conditions on the rows and the columns, we prove that being bounded-below in lp for some 1 ≤ p ≤ ∞, implies that there is a left-inverse which is bounded in lq, for all 1 ≤ q ≤ ∞. In particular, this applies to matrices with polynomial decay, indexed by discrete groups of polyno...

A study on new right/left inverses of nonsquare polynomial matrices

This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called τ -inverses, σ-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The applicationoriented problem of sel...

Computing Moore-Penrose Inverses of Ore Polynomial Matrices

Inverses of Multivariate Polynomial Matrices using Discrete Convolution

A new method for inversion of rectangular matrices in a multivariate polynomial ring with coefficients in a field is explained. This method requires that the polynomial matrix satisfies the one-to-one mapping criteria defined in [1].