• A fast algorithm for scalar Ne...

Treffer: A fast algorithm for scalar Nevanlinna-Pick interpolation

Title:
A fast algorithm for scalar Nevanlinna-Pick interpolation
Authors:
KOC, C. K, CHEN, G
Source:
Numerische Mathematik. 64(1):115-126
Publisher Information:
Berlin; Heidelberg; New York, NY: Springer, 1993.
Publication Year:
1993
Physical Description:
print, 12 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Approximation numérique, Numerical approximation, Algorithme rapide, Fast algorithm, Algoritmo rápido, Complexité calcul, Computing complexity, Complejidad cálculo, Fonction rationnelle, Rational function, Función racional, Fonction variable complexe, Complex variable function, Función variable compleja, Méthode récursive, Recursive method, Método recursivo, Traitement parallèle, Parallel processing, Tratamiento paralelo, CREW PRAM, Interpolation Newaulinna Pick, Tableau Fenyves
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Univ. Houston, dep. electrical eng., Houston TX 77204, United States
ISSN:
0029-599X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=4731273
Rights:
Copyright 1993 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.4731273
Database:
PASCAL Archive

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In this paper, we derive a fast algorithm for the scalar Nevanlinna-Pick interpolation. Given n distinct points zi in the unit disk |z| < 1 and n complex numbers wi satisfying the Pick condition for 1 ≤ i ≤ n, the new Nevanlinna-Pick interpolation algorithm requires only O(n) arithmetic operations to evaluate the interpolatory rational function at a particular value of z, in contrast to the classical algorithm which requires O(n2) arithmetic operations to compute the so-called Fenyves array (which is inherent in the classical algorithm). The new algorithm bypasses the generation of the Fenyves array to speed up the computation, and also yields a parallel scheme requiring only O(log n) arithmetic operations on a concurrent-read, exclusive-write parallel random access machine with n processors.