Title
A stabilized superfast solver for indefinite Hankel systems A stabilized superfast solver for indefinite Hankel systems
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Linear algebra and its applications. - New York, N.Y.
Volume/pages
284(1998) :1-3 , p. 335-355
ISSN
0024-3795
ISI
000076918100017
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We present a stabilized superfast solver for indefinite Hanke1 Systems whose size is a power of 2. The Hanke1 System is transformed into a Loewner System, which is solved by using an inversion formula for Loewner matrices. This explicit formula for the in- Verse of a Loewner matrix contains certain Parameters that are computed by solving two linearized rational interpolation Problems on the unit circle. The heart of our Hankel solver is a superfast algorithm to solve these interpolation Problems. This algorithm is stabilized via pivoting, iterative improvement, and by giving the so-called difficult interpolation Points an adequate treatment. We have implemented our algorithm in Fortran 90. Numerical examples illustrate the effectiveness of our approach.
E-info
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