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

TitleMinimum Distance to the Range of a Banded Lower Triangular Toeplitz Operator in l1 and Application in l1-Optimal Control
Publication TypeJournal Article
Year of Publication2006
AuthorsHurak, Zdenek, Albrecht Böttcher, and Michael Sebek
JournalSIAM Journal on Control and Optimization
Volume45
Issue1
Page107-122
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.

DOI10.1137/S0363012903437940
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