# Minimum Distance to the Range of a Banded Lower Triangular Toeplitz Operator in l1 and Application in l1-Optimal Control

 Title Minimum Distance to the Range of a Banded Lower Triangular Toeplitz Operator in l1 and Application in l1-Optimal Control Publication Type Journal Article Year of Publication 2006 Authors Hurak, Zdenek, Albrecht Böttcher, and Michael Sebek Journal SIAM Journal on Control and Optimization Volume 45 Issue 1 Page 107-122 Abstract The subject of the paper is the best approximation in $\ell^1$ of a given infinite sequence by sequences in the range of a given banded lower-triangular Toeplitz operator. Necessary and sufficient conditions for the existence of a minimizing solution are established and a numerical algorithm for finding such a solution is designed and theoretically founded. It is also shown that an optimal error sequence is only finitely nonzero. The relevancy of the problem in systems theory is outlined and numerical examples are presented. DOI 10.1137/S0363012903437940
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