Minimal degree rational unimodular interpolation on the unit circle

Christer Glader

Minimal degree rational unimodular interpolation on the unit circle

Christer Glader^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

Abstract

We consider an interpolation problem with n distinct nodes z₁, . . . Z_n and n interpolation values w₁ . . ., w _n, all on the complex unit circle, and seek interpolants b(z) of minimal degree in the class consisting of ratios of finite Blaschke products. The focus is on the so-called damaged cases where the interpolant of minimal degree is non-uniquely determined. This paper is a continuation of the work in Glader [Comput. Methods Funct. Theory, 6 (2006), pp. 481-492], which treated the uniquely solvable fragile and elastic cases.

Original language	English
Pages (from-to)	88-106
Number of pages	19
Journal	Electronic Transactions on Numerical Analysis
Volume	30
Publication status	Published - 2008
Externally published	Yes
MoE publication type	A1 Journal article-refereed

Keywords

Blaschke product
Nevanlinna parametrization
Rational interpolation

Cite this

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AB - We consider an interpolation problem with n distinct nodes z1, . . . Zn and n interpolation values w1 . . ., w n, all on the complex unit circle, and seek interpolants b(z) of minimal degree in the class consisting of ratios of finite Blaschke products. The focus is on the so-called damaged cases where the interpolant of minimal degree is non-uniquely determined. This paper is a continuation of the work in Glader [Comput. Methods Funct. Theory, 6 (2006), pp. 481-492], which treated the uniquely solvable fragile and elastic cases.

KW - Blaschke product

KW - Nevanlinna parametrization

KW - Rational interpolation

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JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

SN - 1068-9613

ER -

Minimal degree rational unimodular interpolation on the unit circle

Abstract

Keywords

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