Polynomial perturbations of bilinear functionals and Hessenberg matrices

被引：21

作者：

Bueno, MI ^{[1
]}

Marcellán, F ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 414卷 / 01期

关键词：

perturbation of a bilinear functional; Hessenberg matrix; LU factorization; QR factorization;

D O I：

10.1016/j.laa.2005.09.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：64 / 83

页数：20

共 14 条

[1]

Bueno M.I., 2003, INT MATH J, V3, P319

[2] Continuous symmetrized Sobolev inner products of order N (I) [J].

Bueno, MI ;

Marcellán, F ;

Sánchez-Ruiz, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 306 (01) :83-96

[3] Darboux transformation and perturbation of linear functionals [J].

Bueno, MI ;

Marcellán, F .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 384 :215-242

[4] ON ORTHOGONAL POLYNOMIALS TRANSFORMED BY THE QR ALGORITHM [J].

BUHMANN, MD ;

ISERLES, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1992, 43 (1-2) :117-134

[5]

Chihara T, 1978, INTRO ORTHOGONAL POL

[6] CALCULATION OF GAUSS QUADRATURES WITH MULTIPLE FREE AND FIXED KNOTS [J].

GOLUB, GH ;

KAUTSKY, J .

NUMERISCHE MATHEMATIK, 1983, 41 (02) :147-163

[7]

GRUNBAUM FA, 1997, IMRN INT MAT RES NOT, V8, P359

[8]

GRUNBAUM FA, 1996, CRM P LECT NOTES, V9, P143

[9] DIFFERENTIAL-DIFFERENCE EVOLUTION EQUATIONS .2. (DARBOUX TRANSFORMATION FOR THE TODA LATTICE) [J].

MATVEEV, VB ;

SALLE, MA .

LETTERS IN MATHEMATICAL PHYSICS, 1979, 3 (05) :425-429

[10]

Matveev VB., 1991, DARBOUX TRANSFORMATI

← 1 2 →