The approximation power of moving leastsquares
Author:
David Levin
Journal:
Math. Comp. 67 (1998), 15171531
MSC (1991):
Primary 41A45; Secondary 41A25
MathSciNet review:
1474653
Fulltext PDF Free Access
Abstract 
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Abstract: A general method for nearbest approximations to functionals on , using scattereddata information is discussed. The method is actually the moving leastsquares method, presented by the BackusGilbert approach. It is shown that the method works very well for interpolation, smoothing and derivatives' approximations. For the interpolation problem this approach gives Mclain's method. The method is nearbest in the sense that the local error is bounded in terms of the error of a local best polynomial approximation. The interpolation approximation in is shown to be a function, and an approximation order result is proven for quasiuniform sets of data points.
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 G. Backus and F. Gilbert, 1967 Numerical applications of a formalism for geophysical inverse problems, Geophys. J.R. Astr. Soc. 13 247276.
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 N. Dyn, D. Levin and S. Rippa, 1990 Data dependent triangulation for piecewise linear interpolation, IMA J. Numer. Anal. 10 137154. MR 91a:65022
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Additional Information
David Levin
Affiliation:
School of Mathematical Sciences, TelAviv University, TelAviv 69978, Israel
Email:
levin@math.tau.ac.il
DOI:
http://dx.doi.org/10.1090/S0025571898009740
PII:
S 00255718(98)009740
Received by editor(s):
September 7, 1995
Received by editor(s) in revised form:
September 4, 1996, and March 28, 1997
Article copyright:
© Copyright 1998 American Mathematical Society
