Premium
Stable factorization for Hankel and Hankel‐like matrices
Author(s) -
Olshevsky Vadim,
Stewart Michael
Publication year - 2001
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.252
Subject(s) - mathematics , factorization , hankel matrix , hankel transform , positive definite matrix , stability (learning theory) , displacement (psychology) , class (philosophy) , algorithm , algebra over a field , pure mathematics , mathematical analysis , computer science , fourier transform , eigenvalues and eigenvectors , psychology , physics , quantum mechanics , machine learning , artificial intelligence , psychotherapist
This paper gives fast O ( n 2 ) algorithms for the factorization of positive‐definite and indefinite Hankel matrices. The algorithms are based on the concept of displacement structure and are valid for the more general class of Hankel‐like matrices. The positive‐definite algorithm is proven to be backward stable. The indefinite algorithm uses a look‐ahead step that is naturally suggested by displacement approach. Our error analysis suggests a new criterion for the size of the look‐ahead step and our numerical experiments suggest that the use of the new criterion allows us to ensure numerical stability in practice. Copyright © 2001 John Wiley & Sons, Ltd.