The approximation power of moving least-squares

David Levin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A general method for near-best approximations to functionals on ℝd, 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 ℝd is shown to be a C function, and an approximation order result is proven for quasi-uniform sets of data points.

Original languageEnglish
Pages (from-to)1517-1531
Number of pages15
JournalMathematics of Computation
Issue number224
StatePublished - Oct 1998


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