TY - JOUR

T1 - The approximation power of moving least-squares

AU - Levin, David

PY - 1998/10

Y1 - 1998/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032381035&partnerID=8YFLogxK

U2 - 10.1090/s0025-5718-98-00974-0

DO - 10.1090/s0025-5718-98-00974-0

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AN - SCOPUS:0032381035

SN - 0025-5718

VL - 67

SP - 1517

EP - 1531

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 224

ER -