Computing matrix-valued Nevanlinna-Pick interpolation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)253-263
Journal / PublicationLinear Algebra and Its Applications
Volume203-204
Issue numberC
Publication statusPublished - May 1994
Externally publishedYes

Abstract

We describe a computational method, known as the Nevanlinna algorithm, for the matrix-valued Nevanlinna-Pick interpolation. The original interpolation problem formulated using the Carathéodory class of matrix-valued rational functions is first converted to an equivalent setting using the Schur class of rational functions. As a result, the necessary and sufficient Pick's condition for the interpolation becomes consistent with the scalar-valued formulation, so that some efficient techniques developed for the scalar-valued interpolation can be employed or modified for the matrix-valued case. We give a brief, yet sufficiently clear, derivation and a detailed arithmetic complexity analysis for the algorithm. We show that an n-point matrix-valued Nevanlinna-Pick interpolation using the new algorithm requires approximately 95nm3 complex arithmetic operations, where m is the matrix dimension. © 1994.

Citation Format(s)

Computing matrix-valued Nevanlinna-Pick interpolation. / Chen, Guanrong; Koç, Çetin Kaya.

In: Linear Algebra and Its Applications, Vol. 203-204, No. C, 05.1994, p. 253-263.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review