期刊
IMA JOURNAL OF NUMERICAL ANALYSIS
卷 -, 期 -, 页码 -出版社
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drad086
关键词
best approximation; equioscillation; least squares approximation; polynomial interpolation
In this note, a solution is derived for the problem of finding a polynomial of degree at most $n$ that best approximates data at $n+2$ points in the $l_{p}$ norm. The solution can be expressed as a convex combination of Lagrange interpolants over subsets of $n+1$ points, and the error oscillates in sign.
In this note, we derive a solution to the problem of finding a polynomial of degree at most $n$ that best approximates data at $n+2$ points in the $l_{p}$ norm. Analogous to a result of de la Vallee Poussin, one can express the solution as a convex combination of the Lagrange interpolants over subsets of $n+1$ points, and the error oscillates in sign.
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