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Hermite Interpolation and Sobolev Orthogonality

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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)<

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.

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References

  • Alfaro, M., Pérez, T. E., Piñar, M. A. and Rezola, M. L. (1999)Sobolev orthogonal polynomials: The discrete-continuous case, Methods Appl. Anal. 6(4), 593–616.

    Google Scholar 

  • Chihara, T. S. (1978) An Introduction to Orthogonal Polynomials, Gordon and Breach, New York.

    Google Scholar 

  • Davis, P. J. (1975) Interpolation and Approximation, Dover Publications, New York.

    Google Scholar 

  • Jung, I. H., Kwon, K. H. and Lee, J. K. (1997) Sobolev orthogonal polynomials relative to _p.c/q.c/ C h_; p0.x/q0.x/i, Comm. Korea Math. Soc. 12, 603–627.

    Google Scholar 

  • Kwon, K. H. and Littlejohn, L. L. (1995) The orthogonality of the Laguerre polynomials f._k/ n.x/g for positive integers k, Ann. Numer. Math. 2, 289–304.

    Google Scholar 

  • Kwon, K. H. and Littlejohn, L. L. (1998) Sobolev orthogonal polynomials and second-order differential equations, Rocky Mountain J. Math. 28, 547–594.

    Google Scholar 

  • Marcellán, F., Pérez, T. E., Piñar, M. A. and Ronveaux, A. (1996) General Sobolev orthogonal polynomials, J. Math. Anal. Appl. 200, 614–634.

    Google Scholar 

  • Pérez, T. E. and Piñar, M. A. (1996) On Sobolev orthogonality for the generalized Laguerre polynomials, J. Approx. Theory 86, 278–285.

    Google Scholar 

  • Stoer, J. and Burlirsch, R. (1993) Introduction to Numerical Analysis, 2nd edn, Springer, New York.

  • Szeg?o, G. (1975) Orthogonal Polynomials, 4th edn, Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc., Providence, RI.

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Jaén, Jaén, Spain. e-mail

    Esther M. García-Caballero

  2. Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Spain. e-mail

    Teresa E. Pérez

  3. Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Spain. e-mail

    Miguel A. Piñar

Authors
  1. Esther M. García-Caballero
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  2. Teresa E. Pérez
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  3. Miguel A. Piñar
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García-Caballero, E.M., Pérez, T.E. & Piñar, M.A. Hermite Interpolation and Sobolev Orthogonality. Acta Applicandae Mathematicae 61, 87–99 (2000). https://doi.org/10.1023/A:1006473226163

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