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Matrix-free multilevel moving least-squares methods. (English) Zbl 1028.65011
Chui, Charles K. (ed.) et al., Approximation theory X. Wavelets, splines, and applications. Papers from the 10th international symposium, St. Louis, Mo, USA, March 26-29, 2001. Nashville, TN: Vanderbilt University Press. Innovations in Applied Mathematics. 271-281 (2002).
Summary: We investigate matrix-free formulations for polynomial-based moving least-squares approximation. The well-known method of D. Shepard [A two-dimensional interpolation function for irregularly spaced data, Proc. 23rd Nat. Conf. ACM, 517-523 (1968)] is one such formulation that leads to $$O(h)$$ approximation order. We are interested in methods with higher approximation orders. Several possible approaches are identified, and one of them – based on the analytic solution of small linear systems – is presented here. Numerical experiments with a multilevel residual updating algorithm are also presented.
For the entire collection see [Zbl 1012.00039].

MSC:
 65D15 Algorithms for approximation of functions