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Volume 11, Issue 4
Singularity and Quadrature Regularity of $(0,1,\cdots,m-2,m)$-Interpolation on the Zeros of Jacobi Polynomials

Ying-Guang Shi

J. Comp. Math., 11 (1993), pp. 329-338.

Published online: 1993-11

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  • Abstract

In this paper we show that, if a problem of $(0,1,\cdots,m-2,m)$-interpolation on the zeros of the Jacobi polynomials $P^{\alpha,β}_n(x) (\alpha,β\geq -1)$ has infinite solutions, then the general form of the solutions is $f_0(x)+Cf(x)$ with an arbitrary constant $C$, where $f_0(x)$ and $f(x)$ are fixed polynomials of degree $\leq mn-1$. Moreover, the explicit form of $f(x)$ is given. A necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is also established.  

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@Article{JCM-11-329, author = {Shi , Ying-Guang}, title = {Singularity and Quadrature Regularity of $(0,1,\cdots,m-2,m)$-Interpolation on the Zeros of Jacobi Polynomials}, journal = {Journal of Computational Mathematics}, year = {1993}, volume = {11}, number = {4}, pages = {329--338}, abstract = {

In this paper we show that, if a problem of $(0,1,\cdots,m-2,m)$-interpolation on the zeros of the Jacobi polynomials $P^{\alpha,β}_n(x) (\alpha,β\geq -1)$ has infinite solutions, then the general form of the solutions is $f_0(x)+Cf(x)$ with an arbitrary constant $C$, where $f_0(x)$ and $f(x)$ are fixed polynomials of degree $\leq mn-1$. Moreover, the explicit form of $f(x)$ is given. A necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is also established.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9332.html} }
TY - JOUR T1 - Singularity and Quadrature Regularity of $(0,1,\cdots,m-2,m)$-Interpolation on the Zeros of Jacobi Polynomials AU - Shi , Ying-Guang JO - Journal of Computational Mathematics VL - 4 SP - 329 EP - 338 PY - 1993 DA - 1993/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9332.html KW - AB -

In this paper we show that, if a problem of $(0,1,\cdots,m-2,m)$-interpolation on the zeros of the Jacobi polynomials $P^{\alpha,β}_n(x) (\alpha,β\geq -1)$ has infinite solutions, then the general form of the solutions is $f_0(x)+Cf(x)$ with an arbitrary constant $C$, where $f_0(x)$ and $f(x)$ are fixed polynomials of degree $\leq mn-1$. Moreover, the explicit form of $f(x)$ is given. A necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is also established.  

Ying-Guang Shi. (1970). Singularity and Quadrature Regularity of $(0,1,\cdots,m-2,m)$-Interpolation on the Zeros of Jacobi Polynomials. Journal of Computational Mathematics. 11 (4). 329-338. doi:
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