## The approximation power of moving least-squares

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- by David Levin PDF
- Math. Comp.
**67**(1998), 1517-1531 Request permission

## Abstract:

A general method for near-best approximations to functionals on $\mathbb {R}^d$, 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 $\mathbb {R}^d$ is shown to be a $C^\infty$ function, and an approximation order result is proven for quasi-uniform sets of data points.## References

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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
- Received by editor(s): September 7, 1995
- Received by editor(s) in revised form: September 4, 1996, and March 28, 1997
- © Copyright 1998 American Mathematical Society
- 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