Title
A fast Hankel solver based on an inversion formula for Loewner matrices A fast Hankel solver based on an inversion formula for Loewner matrices
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Publication type
article
Publication
New York, N.Y. ,
Subject
Computer. Automation
Source (journal)
Linear algebra and its applications. - New York, N.Y.
Volume/pages
282(1998) :1-3 , p. 275-295
ISSN
0024-3795
ISI
000076304500017
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We propose a new O(n 2) algorithm for solving complex n × n linear systems that have Hankel structure. Via FFTs the Hankel system is transformed into a Loewner system. An inversion formula enables us to calculate the inverse of the Loewner matrix explicitely. The parameters that occur in this inver,,ion formula are calculated by solving two rational interpolation problems on the unit ~.:ircle. We present an O(n 2) algorithm to solve these interpolation problems. One of the advantages of this algorithm is that it incorporates pivoting. We have implemented our I-I~nkel solver in Fortran 90. Numerical examples are included. They show the effectiveness of our pivoting strategy.
E-info
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