The approximation power of moving least-squares

Mathematics of Computation - Tập 67 Số 224 - Trang 1517-1531
David Levin1
1School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel

Tóm tắt

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

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Tài liệu tham khảo

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Mathematics of Computation

Tập 67 Số 224

1517-1531

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