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 - <p style="text-align: justify;">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. &nbsp;</p>