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Blending-Function Methods of Bivariate and Multivariate Interpolation and Approximation
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1971
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Previous article Blending-Function Methods of Bivariate and Multivariate Interpolation and ApproximationWilliam J. GordonWilliam J. Gordonhttps://doi.org/10.1137/0708019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. H. Ahlberg, , E. N. Nilson and , J. L. Walsh, The theory of splines and their applications, Academic Press, New York, 1967xi+284 MR0239327 0158.15901 Google Scholar[2] A. C. Ahlin, A bivariate generalization of Hermite's interpolation formula, Math. Comp., 18 (1964), 264–273 MR0164428 0122.12501 CrossrefISIGoogle Scholar[3] R. E. Barnhill, , W. J. Gordon and , D. H. Thomas, Decomposition methods for the approximate integration of multivariate functions, Res. Rep., General Motors, Warren, Mich., in preparation Google Scholar[4] Garrett Birkhoff and , Carl R. De Boor, H. L. Garabedian, Piecewise polynomial interpolation and approximation, Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964 ), Elsevier Publ. Co., Amsterdam, 1965, 164–190 MR0189219 0136.04703 Google Scholar[5] Garrett Birkhoff and , William J. Gordon, The draftsman's and related equations, J. Approximation Theory, 1 (1968), 199–208 10.1016/0021-9045(68)90024-5 MR0235752 0189.40902 CrossrefGoogle Scholar[6] Garrett Birkhoff and , Saunders Mac Lane, A survey of modern algebra, Macmillan Co., New York, N. Y., 1953xi+472 MR0054551 0052.25402 Google Scholar[7] Garrett Birkhoff and , Gian-Carlo Rota, Ordinary differential equations, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, 1962vii+318 MR0138810 0102.29901 Google Scholar[8] R. C. Buck, Advanced Calculus, McGraw-Hill, New York, 1965 0125.30102 Google Scholar[9] S. A. Coons, Surfaces for Computer Aided Design of Space Forms, Project MAC, Design Div., Dept. of Mech. Engineering, MIT, 1964, Revised to MAC-TR-41, 1967. Available from CFSTI, Sills Building, 5285 Port Royal Road, Springfield, Virginia, 22151 Google Scholar[10] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963xiv+393 MR0157156 0111.06003 Google Scholar[11] Carl de Boor, Bicubic spline interpolation, J. Math. and Phys., 41 (1962), 212–218 MR0158512 0108.27103 CrossrefISIGoogle Scholar[12] Carl de Boor and , Robert E. Lynch, On splines and their minimum properties, J. Math. Mech., 15 (1966), 953–969 MR0203306 0185.20501 ISIGoogle Scholar[13] James Ferguson, Multivariable curve interpolation, J. Assoc. Comput. Mach., 11 (1964), 221–228 MR0162352 0123.33004 CrossrefISIGoogle Scholar[14] A. R. Forrest, Masters Thesis, Curves and surfaces for computer-aided design, Doctoral thesis, The University Mathematical Laboratory, Cambridge Univ., Cambridge, England, 1968 Google Scholar[15] A. R. Forrest, Coons surfaces and multivariable functional interpolation, 1971, J. Assoc. Comput. Mach., to appear Google Scholar[16] William J. Gordon, Spline-blended surface interpolation through curve networks, J. Math. Mech., 18 (1968/1969), 931–952 MR0246027 0192.42201 ISIGoogle Scholar[17] William J. Gordon, Blending: function methods of bivariate and multivariate interpolation and approximation, Res. Rep., GMR-834, General Motors, Warren, Mich., 1968 Google Scholar[18] William J. Gordon, I. J. Schoenberg, Distributive lattices and the approximation of multivariate functionsApproximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., 1969), Academic Press, New York, 1969, 223–277 MR0275021 0269.41029 Google Scholar[19] William J. Gordon, Free form surface interpolation through curve networks, Res. Rep., GMR-921, General Motors, Warren, Mich., 1969 Google Scholar[20] E. L. Ince, Ordinary Differential Equations, Dover, New York, 1956 Google Scholar[21] W. L. Johnson, Analytic surfaces for computer-aided design, Paper 660152, Proc. 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Anal., 1 (1964), 137–163 MR0177240 0143.07901 LinkGoogle Scholar Previous article FiguresRelatedReferencesCited byDetails Higher order theories for the free vibration analysis of laminated anisotropic doubly-curved shells of arbitrary geometry with general boundary conditionsComposite Structures, Vol. 297 Cross Ref A revisit to smoothness preserving fractal perturbation of a bivariate function: Self-Referential counterpart to bicubic splinesChaos, Solitons & Fractals, Vol. 157 Cross Ref Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks10 February 2022 | Mathematics, Vol. 10, No. 4 Cross Ref Generalized higher order layerwise theory for the dynamic study of anisotropic doubly -curved shells with a mapped geometryEngineering Analysis with Boundary Elements, Vol. 134 Cross Ref High order transition elements: The xy-element concept, Part II: DynamicsComputer Methods in Applied Mechanics and Engineering, Vol. 387 Cross Ref Multilevel quadrature for 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