TY - JOUR

T1 - A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices

AU - Bella, Tom

AU - Eidelman, Yuli

AU - Gohberg, Israel

AU - Koltracht, Israel

AU - Olshevsky, Vadim

N1 - Funding Information:
Keywords: Björck–Pereyra algorithm; Szegö polynomials; Unitary Hessenberg matrices; Vandermonde matrices; Polynomial-Vandermonde matrices; Fast algorithms Supported by the NSF grant 0242518. ∗ Corresponding author. E-mail addresses: bella@math.uconn.edu (T. Bella), eideyu@post.tau.ac.il (Y. Eidelman), gohberg@post.tau.ac.il (I. Gohberg), koltracht@math.uconn.edu (I. Koltracht), olshevsky@math.uconn.edu (V. Olshevsky).

PY - 2007/1/15

Y1 - 2007/1/15

N2 - In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems VΦ(x), i.e., polynomial-Vandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n2) computational procedure. We present numerical experiments that indicate that for ill-conditioned matrices the new algorithm yields better forward accuracy than Gaussian elimination.

AB - In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems VΦ(x), i.e., polynomial-Vandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n2) computational procedure. We present numerical experiments that indicate that for ill-conditioned matrices the new algorithm yields better forward accuracy than Gaussian elimination.

KW - Bjorck-pereyra algorithm

KW - Polynomial-Vandermonde matrices

KW - Szegö polynomials

KW - Unitary hessenberg matrices

KW - Vandermonde matrices

KW - fast algorithms

UR - http://www.scopus.com/inward/record.url?scp=33750989081&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2006.08.032

DO - 10.1016/j.laa.2006.08.032

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AN - SCOPUS:33750989081

SN - 0024-3795

VL - 420

SP - 634

EP - 647

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -