Haussmann, Werner On multivariate spline systems. (English) Zbl 0292.41009 J. Approximation Theory 11, 285-305 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 41A15 Spline approximation 41A63 Multidimensional problems PDF BibTeX XML Cite \textit{W. Haussmann}, J. Approx. Theory 11, 285--305 (1974; Zbl 0292.41009) Full Text: DOI References: [1] Anselone, P. M.; Laurent, P. J., A general method for the construction of interpolating or smoothing spline-functions, Numer. Math., 12, 66-82 (1968) · Zbl 0197.13501 [2] Atteia, M., Généralisation de la définition et des propriétés des “spline fonctions,”, C. R. Acad. Sci. Paris, 260, 3550-3553 (1965) · Zbl 0163.37703 [3] Atteia, M., “Spline fonctions” généralisées, C. R. Acad. Sci. Paris, 261, 2149-2152 (1965) · Zbl 0127.06601 [4] Aubin, J. P., Interpolation et approximation optimales et “spline fonctions,”, J. Math. Anal. Appl., 24, 1-24 (1968) · Zbl 0188.43702 [5] Birkhoff, G.; Schultz, M. H.; Varga, R. S., Piecewisc Hermite interpolation in one and two variables with applications to partial differential equations, Numer. Math., 11, 232-256 (1968) · Zbl 0159.20904 [6] de Boor, C. R., Bicubic spline interpolation, J. Math. Phys., 41, 212-218 (1962) · Zbl 0108.27103 [7] de Boor, C. R.; Lynch, R. E., On splines and their minimum properties, J. Math. Mech., 15, 953-969 (1966) · Zbl 0185.20501 [8] Davis, P. J., Interpolation and Approximation (1965), Blaisdell: Blaisdell New York · Zbl 0111.06003 [9] Delvos, F. J.; Schempp, W., On spline systems, Monatsh. Math., 74, 399-409 (1970) · Zbl 0203.12202 [10] Delvos, F. J.; Schempp, W., On spline systems: \(L_m\)-splines, Math. Z., 126, 154-170 (1972) · Zbl 0222.41006 [11] Dixmier, J., Les algèbres d’opérateurs dans l’espace Hilbertien (1957), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0088.32304 [12] Gordon, W. J., Spline-blended surface interpolation through curve networks, J. Math. Mech., 18, 931-952 (1969) · Zbl 0192.42201 [13] Greub, W. H., Multilinear Algebra (1967), Springer: Springer Berlin/Heidelberg/New York · Zbl 0169.35302 [14] Greville, T. N.E, Spline functions, interpolation and numerical quadrature, (Ralston, A.; Wilf, H. S., Mathematical Methods for Digital Computers, Vol. 2 (1967), Wiley: Wiley New York), 156-168 · Zbl 0312.65007 [15] Haussmann, W., Tensorprodukte und mehrdimensionale Interpolation, Math. Z., 113, 17-23 (1970) · Zbl 0183.05902 [16] Haussmann, W., Zur Theorie der Spline-Systeme, Habilitationsschrift (1970), Ruhr-Universität Bochum: Ruhr-Universität Bochum Bochum [17] Haussmann, W., Tensorproduktmethoden bei mehrdimensionaler Interpolation, Math. Z., 124, 191-198 (1972) · Zbl 0226.41007 [18] Jerome, J. W.; Schumaker, L. L., On Lg-splines, J. Approximation Theory, 2, 29-49 (1969) · Zbl 0172.34501 [19] Jerome, J. W.; Varga, R. S., Generalizations of spline functions and applications to nonlinear boundary value and eigenvalue problems, (Greville, T. N.E, Theory and Applications of Spline Functions (1969), Academic Press: Academic Press New York/London), 103-155 · Zbl 0188.13004 [20] Lucas, T. R., M-splines, J. Approximation Theory, 5, 1-14 (1972) · Zbl 0227.41002 [21] Mansfield, L. E., Optimal approximation and error bounds in spaces of bivariate functions, J. Approximation Theory, 5, 77-96 (1972) · Zbl 0247.41012 [22] Ritter, K., Two-dimensional splines and their extremal properties, Z. Angew. Math. Mech., 49, 597-608 (1969) · Zbl 0194.09502 [23] Ritter, K., Two-dimensional spline functions and best approximation of linear functionals, J. Approximation Theory, 3, 352-368 (1970) · Zbl 0203.37001 [24] Sard, A., Optimal approximation, J. Functional Anal., 2, 368-369 (1968) · Zbl 0159.43801 [25] Schatten, R., A Theory of Cross Spaces, (Annals of Math. Studies Nr. 28 (1950), Princeton University Press: Princeton University Press Princeton, NJ) · Zbl 0041.43502 [27] Schultz, M. H., Multivariate \(L\)-spline interpolation, J. Approximation Theory, 2, 127-135 (1969) · Zbl 0202.34901 [28] Schultz, M. H.; Varga, R. S., \(L\)-splines, Numer. Math., 10, 345-369 (1967) · Zbl 0183.44402 [29] Tippenhauer, U., Mehrdimensionale invariante Interpolationssysteme in Hilbert-räumen, Z. Angew. Math. Mech., 52, T222-T224 (1972) · Zbl 0235.65005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.