$(0,1,\cdots,m-2,m)$ Interpolation for the Laguerre Abscissas

$(0,1,\cdots,m-2,m)$ Interpolation for the Laguerre Abscissas

Year:    1994

Author:    Ying-Guang Shi

Journal of Computational Mathematics, Vol. 12 (1994), Iss. 2 : pp. 123–131

Abstract

A necessary and sufficient condition of regularity of $(0,1,\cdots,m-2,m)$ interpolation on the zeros of Laguerre polynomials $L_n^{(α)}(x) (α≥-1)$ in a manageable form is established. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given. Moreover, it is shown that, if the problem of $(0,1,\cdots,m-2,m)$ interpolation has an infinity of solutions, then the general form of the solutions is $f_0(x)+Cf_1(x)$ with an arbitrary constant $C$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1994-JCM-9281

Journal of Computational Mathematics, Vol. 12 (1994), Iss. 2 : pp. 123–131

Published online:    1994-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    9

Keywords:   

Author Details

Ying-Guang Shi