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Volume 12, Issue 3
$(0,1,\cdots,m-2,m)$ Interpolation for the Laguerre Abscissas

Ying-Guang Shi

J. Comp. Math., 12 (1994), pp. 239-247.

Published online: 1994-12

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  • Abstract

A necessary and sufficient condition of regularity of $(0,1,\cdots,m-2,m)$ interpolation on the zeros of Laguerre polynomials $L^{(α)}_n(x) (α≥-1)$ 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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@Article{JCM-12-239, author = {Shi , Ying-Guang}, title = {$(0,1,\cdots,m-2,m)$ Interpolation for the Laguerre Abscissas}, journal = {Journal of Computational Mathematics}, year = {1994}, volume = {12}, number = {3}, pages = {239--247}, abstract = {

A necessary and sufficient condition of regularity of $(0,1,\cdots,m-2,m)$ interpolation on the zeros of Laguerre polynomials $L^{(α)}_n(x) (α≥-1)$ 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 $C$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9295.html} }
TY - JOUR T1 - $(0,1,\cdots,m-2,m)$ Interpolation for the Laguerre Abscissas AU - Shi , Ying-Guang JO - Journal of Computational Mathematics VL - 3 SP - 239 EP - 247 PY - 1994 DA - 1994/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9295.html KW - AB -

A necessary and sufficient condition of regularity of $(0,1,\cdots,m-2,m)$ interpolation on the zeros of Laguerre polynomials $L^{(α)}_n(x) (α≥-1)$ 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 $C$.

Shi , Ying-Guang. (1994). $(0,1,\cdots,m-2,m)$ Interpolation for the Laguerre Abscissas. Journal of Computational Mathematics. 12 (3). 239-247. doi:
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