The approximation power of moving least-squares

Author:
David Levin

Journal:
Math. Comp. **67** (1998), 1517-1531

MSC (1991):
Primary 41A45; Secondary 41A25

DOI:
https://doi.org/10.1090/S0025-5718-98-00974-0

MathSciNet review:
1474653

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Abstract: A general method for near-best approximations to functionals on , using scattered-data information is discussed. The method is actually the moving least-squares method, presented by the Backus-Gilbert 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 near-best 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 quasi-uniform sets of data points.

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Additional Information

**David Levin**

Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel

Email:
levin@math.tau.ac.il

DOI:
https://doi.org/10.1090/S0025-5718-98-00974-0

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