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Uniform approximation on the sphere by least squares polynomials
- Source :
- Numerical algorithms 81 (2019): 1089–1111. doi:10.1007/s11075-018-0584-1, info:cnr-pdr/source/autori:Themistoclakis W.; Van Barel M./titolo:Uniform approximation on the sphere by least squares polynomials/doi:10.1007%2Fs11075-018-0584-1/rivista:Numerical algorithms/anno:2019/pagina_da:1089/pagina_a:1111/intervallo_pagine:1089–1111/volume:81
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- The paper concerns the uniform polynomial approximation of a function $f$, continuous on the unit Euclidean sphere of ${\mathbb R}^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First we focus on least squares polynomial approximation and prove that the related Lebesgue constants w.r.t. the uniform norm grow at the optimal rate. Then, we consider delayed arithmetic means of least squares polynomials whose degrees vary from $n-m$ up to $n+m$, being $m=\lfloor \theta n\rfloor$ for any fixed parameter $0<br />Comment: 20 pages
- Subjects :
- De la Vallée Poussin type mean
Polynomial
Pure mathematics
Polynomial approximation on the sphere
010103 numerical & computational mathematics
Lebesgue integration
01 natural sciences
Least squares
Minimax approximation algorithm
41-A10, 65-D99, 33-C45
Uniform approximation
symbols.namesake
Uniform norm
uniform approximation
FOS: Mathematics
polynomial approximation on the sphere
Mathematics - Numerical Analysis
0101 mathematics
Finite set
Mathematics
Applied Mathematics
Numerical analysis
Lebesgue constant
Numerical Analysis (math.NA)
Function (mathematics)
010101 applied mathematics
Least squares approximation
least squares approximation
symbols
de la Vallée Poussin type mean
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 81
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....5c06b5dda7b9494d3451d31658f16f25