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Surfaces generated by moving least squares methods. (English) Zbl 0469.41005

MSC:
41A05 Interpolation in approximation theory
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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[1] Robert E. Barnhill, Representation and approximation of surfaces, Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1977) Academic Press, New York, 1977, pp. 69 – 120. Publ. Math. Res. Center Univ. Wisconsin, No. 39. · Zbl 0407.68030
[2] 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.
[3] Richard Franke and Greg Nielson, Smooth interpolation of large sets of scattered data, Internat. J. Numer. Methods Engrg. 15 (1980), no. 11, 1691 – 1704. · Zbl 0444.65011 · doi:10.1002/nme.1620151110 · doi.org
[4] William J. Gordon and James A. Wixom, Shepard’s method of ”metric interpolation” to bivariate and multivariate interpolation, Math. Comp. 32 (1978), no. 141, 253 – 264. · Zbl 0383.41003
[5] Peter Lancaster, Moving weighted least-squares methods, Polynomial and spline approximation (Proc. NATO Adv. Study Inst., Univ. Calgary, Calgary, Alta., 1978) NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 49, Reidel, Dordrecht-Boston, Mass., 1979, pp. 103 – 120.
[6] Peter Lancaster, Composite methods for generating surfaces, Polynomial and spline approximation (Proc. NATO Adv. Study Inst., Univ. Calgary, Calgary, Alta., 1978) NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 49, Reidel, Dordrecht-Boston, Mass., 1979, pp. 91 – 102.
[7] D. H. Mclain, ”Drawing contours from arbitrary data points,” Comput. J., v. 17, 1974, pp. 318-324.
[8] Lois Mansfield, Higher order compatible triangular finite elements, Numer. Math. 22 (1974), 89 – 97. · Zbl 0265.65011 · doi:10.1007/BF01436723 · doi.org
[9] M. J. D. Powell and M. A. Sabin, Piecewise quadratic approximations on triangles, ACM Trans. Math. Software 3 (1977), no. 4, 316 – 325. · Zbl 0375.41010 · doi:10.1145/355759.355761 · doi.org
[10] S. Ritchie, Representation of Surfaces by Finite Elements, M.Sc. Thesis, University of Calgary, 1978.
[11] D. Shepard, A Two-Dimensional Interpolation Function for Irregularly Spaced Points, Proc. 1968 A.C.M. Nat. Conf., pp. 517-524.
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