The eigenvalues of matrices that occur in certain interpolation problems

Author

Ferreira, Paulo J S G

Author_Institution

Dept. de Electron. e Telecoms, Aveiro Univ., Portugal

Volume

45

Issue

8

fYear

1997

fDate

8/1/1997 12:00:00 AM

Firstpage

2115

Lastpage

2120

Abstract

The eigenvalues of the matrices that occur in certain finite-dimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots, that is, on the sampling set. We study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the interpolation matrices. The bounds can be evaluated in as few as four arithmetic operations, and therefore, they greatly simplify the assessment of sampling sets regarding numerical stability. The accuracy and usefulness of the bounds are illustrated with examples

Keywords

eigenvalues and eigenfunctions; interpolation; matrix algebra; numerical stability; signal sampling; eigenvalues; finite-dimensional interpolation problems; interpolation knots; interpolation matrices; numerical stability; sampling set; signal processing; Arithmetic; Bandwidth; Eigenvalues and eigenfunctions; Image sampling; Interpolation; Iterative algorithms; Numerical stability; Sampling methods; Signal processing algorithms; Signal sampling;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.611226

Filename

611226