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Title: Orthogonal rational functions on the unit circle: from the scalar to the matrix case
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav
Issue Date: Jul-2004
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW401
Abstract: The purpose of these lecture notes is to give a short introduction to the theory of orthogonal rational functions (ORF) on the unit circle. We start with the classical problem of linear prediction of a stochastic process to give a motivation for the study of Szego's problem and to show that in this context it will turn out that not as much the ORF but rather the reproducing kernels will play a central role. Another example of rational Krylov iteration shows that it might also be interesting to consider ORF on the real line, which we shall not discuss in these lectures.
URI: 
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
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