# Approximation by Banded Matrices and Application to Wireless Communications

Andreas Klotz

given at  strobl07 (19.06.07)
id:  832
length:  min
status:  accepted
type:  poster
ABSTRACT:

TeX:
Banach algebras of matrices $A(i,k)_{i,k \in \Z^d}$ with some kind of off-diagonal decay arise naturally in applications. Starting points of our research have been the following questions:

{Can off diagonal decay of matrices be characterized by the quality of approximation'' with banded matrices (matrices with $A(i,k)=0$ if $\abs{i-k}>n$ for an $n$)?}

This falls into the framework of approximation theory.

{Do the approximation spaces of matrix algebras inherit special properties? Are they, in particular, again Banach Algebras s? Does a matrix inverse $A^{-1}$ have the same approximation quality as $A$? }

This asks for \emph{spectral invariance} properties of the approximation spaces.

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