Surfaces generated by moving least squares methods

Mathematics of Computation - Tập 37 Số 155 - Trang 141-158
Peter Lancaster, K. Šalkauskas

Tóm tắt

An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analysis is accompanied by examples of univariate and bivariate problems.

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Tài liệu tham khảo

Barnhill, Robert E., 1977, Representation and approximation of surfaces, 69

R. W. Clough & J. L. Tocher, "Finite element stiffness matrices for analysis of plates in bending," in Proc. Conf. Matrix Methods in Structural Mechanics, Wright-Patterson A.F.B., Ohio, 1965.

Franke, Richard, 1980, Smooth interpolation of large sets of scattered data, Internat. J. Numer. Methods Engrg., 15, 1691, 10.1002/nme.1620151110

Gordon, William J., 1978, Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation, Math. Comp., 32, 253, 10.2307/2006273

Lancaster, Peter, 1979, Moving weighted least-squares methods, 103

Lancaster, Peter, 1979, Composite methods for generating surfaces, 91

D. H. Mclain, "Drawing contours from arbitrary data points," Comput. J., v. 17, 1974, pp. 318-324.

Mansfield, Lois, 1974, Higher order compatible triangular finite elements, Numer. Math., 22, 89, 10.1007/BF01436723

Powell, M. J. D., 1977, Piecewise quadratic approximations on triangles, ACM Trans. Math. Software, 3, 316, 10.1145/355759.355761

S. Ritchie, Representation of Surfaces by Finite Elements, M.Sc. Thesis, University of Calgary, 1978.

D. Shepard, A Two-Dimensional Interpolation Function for Irregularly Spaced Points, Proc. 1968 A.C.M. Nat. Conf., pp. 517-524.