On tangential matrix interpolation

P. A. Fuhrmann

doi:10.1016/j.laa.2010.07.018

On tangential matrix interpolation

P. A. Fuhrmann

Department of Mathematics

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

2 Scopus citations

Abstract

The paper presents an algebraic approach, using polynomial and rational models over an arbitrary field, to tangential interpolation problems, both by polynomial as well as rational matrix functions. Appropriate extensions of scalar problems, associated with the names of Lagrange (first order), Hermite (high order) and Newton (recursive) are derived. The relation of interpolation problems to the matrix Chinese remainder theorem are clarified. Some two sided interpolation problems are discussed, using the theory of tensored functional models.

Original language	English
Pages (from-to)	2018-2059
Number of pages	42
Journal	Linear Algebra and Its Applications
Volume	433
Issue number	11-12
DOIs	https://doi.org/10.1016/j.laa.2010.07.018
State	Published - 30 Dec 2010

Keywords

Chinese remainder theorem
Functional models
Tangential interpolation

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2010.07.018

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N2 - The paper presents an algebraic approach, using polynomial and rational models over an arbitrary field, to tangential interpolation problems, both by polynomial as well as rational matrix functions. Appropriate extensions of scalar problems, associated with the names of Lagrange (first order), Hermite (high order) and Newton (recursive) are derived. The relation of interpolation problems to the matrix Chinese remainder theorem are clarified. Some two sided interpolation problems are discussed, using the theory of tensored functional models.

AB - The paper presents an algebraic approach, using polynomial and rational models over an arbitrary field, to tangential interpolation problems, both by polynomial as well as rational matrix functions. Appropriate extensions of scalar problems, associated with the names of Lagrange (first order), Hermite (high order) and Newton (recursive) are derived. The relation of interpolation problems to the matrix Chinese remainder theorem are clarified. Some two sided interpolation problems are discussed, using the theory of tensored functional models.

KW - Chinese remainder theorem

KW - Functional models

KW - Tangential interpolation

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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ER -

On tangential matrix interpolation

Abstract

Keywords

ASJC Scopus subject areas

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