Domain of validity of Szegö quadrature formulas

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• 作者：O. NjÅ ; stad ; J.C. Santos-Leó ; n
• 关键词：Domain of validity ; Orthogonal polynomials ; Szeg&#xf6 ; quadrature formulas
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2007
• 期刊代码：72_03770427
• 类别：cp
• 出版时间：15 May 2007
• 卷：202
• 期：2
• 页码：440-449
• 文件大小：173 K

摘要

As is well known, the n-point Szegö quadrature formula integrates correctly any Laurent polynomial in the subspace span{JRVDX9-G&_mathId=mml1&_user=10&_cdi=5619&_rdoc=24&_acct=C000050221&_version=1&_userid=10&md5=c0476fb00d971f9ea7236b25c0c9c73a" title="Click to view the MathML source">1/z^n-1,…,1/z,1,z,…,z^n-1}. In this paper we enlarge this subspace. We prove that a set of 2n linearly independent Laurent polynomials are integrated correctly. The obtained result is used for the construction of Szegö quadrature formulas. Illustrative examples are given.