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

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• 作者：Tom Bella ; Yuli Eidelman ; Israel Gohberg ; Israel Koltracht ; Vadim Olshevsky
• 关键词：Bjorck-pereyra algorithm ; Szegö ; polynomials ; Unitary hessenberg matrices ; Vandermonde matrices ; Polynomial-Vandermonde matrices ; fast algorithms
• 刊名：Linear Algebra and its Applications
• 出版年：2007
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：15 January 2007
• 卷：420
• 期：2-3
• 页码：634-647
• 文件大小：185 K

摘要

In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems V_Φ(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.