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Barrio, R.; Melendo, B.; Serrano, S.

Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. I: Algorithms. (English) Zbl 1066.42017

J. Comput. Appl. Math. 181, No. 2, 280-298 (2005).
Summary: We study theoretically the determination and evaluation of polynomials that are orthogonal with respect to a general discrete Sobolev inner product, that is, an ordinary inner product on the real line plus a finite sum of atomic inner products involving a finite number of derivatives. This Sobolev inner product has the property that the orthogonal polynomials with respect to it satisfy a linear recurrence relation of fixed order. We provide a complete set of formulas to compute the coefficients of this recurrence. Besides, we study the determination of the Fourier-Sobolev coefficients of a finite approximation of a function and the numerical evaluation of the resulting finite series at a general point.

Cited in 1 Review
Cited in 4 Documents

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
65D20 Computation of special functions and constants, construction of tables
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
33C47 Other special orthogonal polynomials and functions

Keywords:

Sobolev orthogonal polynomials; recurrence relations; Fourier-Sobolev coefficients; approximation; numerical evaluation

Software:

ORTHPOL
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Full Text: DOI

References:

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