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Meinguet, Jean

Multivariate interpolation at arbitrary points made simple. (English) Zbl 0428.41008

Z. Angew. Math. Phys. 30, 292-304 (1979).
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Cited in 58 Documents

MSC:

41A15 Spline approximation
41A05 Interpolation in approximation theory
41A50 Best approximation, Chebyshev systems

Keywords:

multivariate interpolation; surface spline interpolation; Sobolev seminorm; numerical stability of Cholesy factorization
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\textit{J. Meinguet}, Z. Angew. Math. Phys. 30, 292--304 (1979; Zbl 0428.41008)
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References:

[1] J. H. Ahlberg, E. N. Nilson, andJ. L. Walsh,The Theory of Splines and Their Applications, Academic Press Inc., New York (1967). · Zbl 0158.15901
[2] A. C. Aitken,Determinants and Matrices, Oliver and Boyd Ltd., Edinburgh (1956).
[3] P. J. Davis,Interpolation and Approximation, Blaisdell Publ. Co., New York (1963). · Zbl 0111.06003
[4] C. de Boor andR. E. Lynch,On Splines and their Minimum Properties, J. Math. Mech.15, 953–969 (1966). · Zbl 0185.20501
[5] J. Duchon,Fonctions-spline à énergie invariante par rotation, Rapport de recherche no 27, Université de Grenoble (1976).
[6] J. Duchon,Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, R.A.I.R.O. Analyse numérique10, 5–12 (1976).
[7] J. Duchon, ’Splines Minimizing Rotation–Invariant Semi-norms in Sobolev Spaces’, inConstructive Theory of Functions of Several Variables, Oberwolfach 1976, W. Schempp and K. Zeller, ed., pp. 85–100, Springer-Verlag, Berlin-Heidelberg (1977).
[8] M. Golomb andH. F. Weinberger, ’Optimal Approximation and Error Bounds’, inOn Numerical Approximation, R. E. Langer, ed., pp. 117–190, The University of Wisconsin Press, Madison (1959). · Zbl 0092.05802
[9] R. L. Harder andR. N. Desmarais,Interpolation Using Surface Splines, J. Aircraft9, 189–191 (1972).
[10] J. Meinguet,Optimal Approximation and Error Bounds in Seminormed Spaces, Num. Math.10, 370–388 (1967). · Zbl 0261.65009
[11] J. Meinguet, ’An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points’. To appear inProc. NATO Advanced Study Institute on Polynomial and Spline Approximation, Calgary 1978, B. N. Sahney, ed., 29 pp., D. Reidel Publ. Co., Dordrecht (1979). · Zbl 0444.41009
[12] H. S. Shapiro,Topics in Approximation Theory, Springer-Verlag, Berlin-Heidelberg (1971). · Zbl 0213.08501
[13] H. W. Turnbull,The Theory of Determinants, Matrices, and Invariants, Dover Publ., Inc., New York (1960). · Zbl 0103.00702
[14] B. Wendroff,Theoretical Numerical Analysis, Academic Press Inc., New York (1966). · Zbl 0141.32805
[15] J. H. Wilkinson andC. Reinsch,Linear Algebra, Springer-Verlag, Berlin-Heidelberg (1971).
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.