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Polynomial perturbations of bilinear functionals and Hessenberg matrices

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URI: https://hdl.handle.net/10016/5941
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.09.010
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polynomial_marcellan_laa_2006_ps.pdf (425.53 KB)
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2006-04-01
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Elsevier
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Abstract
This paper deals with symmetric and non-symmetric polynomial perturbations of symmetric quasi-definite bilinear functionals. We establish a relation between the Hessenberg matrices associated with the initial and the perturbed functionals using LU and QR factorizations. Moreover we give an explicit algebraic relation between the sequences of orthogonal polynomials associated with both functionals.
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20 pages, no figures.-- MSC2000 codes: 42C05; 15A23.
MR#: MR2209234 (2008c:42024)
Zbl#: Zbl 1134.42015
Keywords
Perturbation of a bilinear functional, Hessenberg matrix, LU factorization, QR factorization
Bibliographic citation
Linear Algebra and its Applications, 2006, vol. 141, n. 1, p. 64-83
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