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Hermite Interpolation and Sobolev Orthogonality (2000)

García-Caballero, Esther M. ; Pérez, Teresa E. ; Piñar, Miguel A.

Springer

Acta applicandae mathematicae 61 (2000), S. 87-99

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ISSN: 1572-9036

Keywords: Sobolev bilinear forms ; orthogonal polynomials ; Hermite interpolation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g) S = V(f) A V(g) T + 〈u, f (N) g (N)〈 where V(f) =(f(c 0), f "(c 0), ..., f (n − 1) 0(c 0), ..., f(c p ), f "(c p ), ..., f (n − 1) p(c p )) u is a regular linear functional on the linear space P of real polynomials, c 0, c 1, ..., c p are distinct real numbers, n 0, n 1, ..., n p are positive integer numbers, N=n 0+n 1+...+n p , and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1006473226163

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