Optimal Lagrange Interpolation of a Class of Infinitely Differentiable Functions |
Received:November 09, 2020 Revised:January 03, 2021 |
Key Words:
worst case setting optimal Lagrange interpolation infinitely differentiable function space
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Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11871006). |
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Abstract: |
This paper investigates the optimal Lagrange interpolation of a class $F_\infty$ of infinitely differentiable functions on $[-1,1]$ in $L_\infty[-1,1]$ and weighted spaces $L_{p,\omega}[-1,1], \ 1\le p< \infty$ with $\omega$ a continuous integrable weight function in $(-1,1)$. We proved that the Lagrange interpolation polynomials based on the zeros of polynomials with the leading coefficient $1$ of the least deviation from zero in $L_{p,\omega}[-1,1]$ are optimal for $1\le p<\infty$. We also give the optimal Lagrange interpolation nodes when the endpoints are included in the nodes. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2021.06.007 |
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