Hermite Interpolation and Sobolev Orthogonality |
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| Authors: | Esther M. García-Caballero Teresa E. Pérez Miguel A. Piñar |
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| Affiliation: | (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) AV(g)T + <u, f(N)g(N)V(f) =(f(c0), f "(c0), ..., f(n – 1)0(c0), ..., f(cp), f "(cp), ..., f(n – 1)p(cp))u is a regular linear functional on the linear space P of real polynomials, c0, c1, ..., cp are distinct real numbers, n0, n1, ..., np are positive integer numbers, N=n0+n1+...+np, 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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