Hermite Interpolation and Sobolev Orthogonality |
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| Authors: | Esther M García-Caballero Teresa E Pérez Miguel A Piñar |
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| Institution: | (1) Departamento de Matemáticas, Universidad de Jaén, Jaén, Spain. e-mail;(2) Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Spain. e-mail;(3) Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Spain. e-mail |
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| 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)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. |
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| Keywords: | Sobolev bilinear forms orthogonal polynomials Hermite interpolation |
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