Surfaces generated by moving least squares methods
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.
Từ khóa
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
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.
