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An algorithm for cubic spline fitting with convexity constraints. (English) Zbl 0419.65006


MSC:

65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
90C20 Quadratic programming
65-04 Software, source code, etc. for problems pertaining to numerical analysis
41A15 Spline approximation
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References:

[1] Amos, D. E., Slater, M. L.: Polynomial and spline approximation by quadratic programming. C.A.C.M.12, 379–381 (1969). · Zbl 0187.12704
[2] Boot, J. C. G.: Quadratic programming, pp. 95–117. Chicago: Rand Mc Nally 1964. · Zbl 0138.15802
[3] Carasso, C.: Méthodes numériques pour l’obtention de fonctions spline. Thèse de 3ème cycle, Université de Grenoble, 1966.
[4] Cox, M. G.: The numerical evaluation of B-splines. J. Inst. Maths. Applics10, 134–144 (1972). · Zbl 0252.65007 · doi:10.1093/imamat/10.2.134
[5] Cox, M. G.: Cubic spline fitting with convexity and concavity constraints. National Physical Laboratory Report NAC 23. Teddington, Middlesex 1973.
[6] Curry, H. B., Schoenberg, I. J.: On Polya frequency functions IV. J. Analyse Math.17, 71–107 (1966). · Zbl 0146.08404 · doi:10.1007/BF02788653
[7] DeBoor, C.: On calculating with B-splines. J. Approx. Theory6, 50–62 (1972). · Zbl 0239.41006 · doi:10.1016/0021-9045(72)90080-9
[8] Greville, T. N. E.: Introduction to spline functions. Theory and applications of spline functions (Greville, T. N. E., ed.), pp. 1–35. New York: Academic Press 1969. · Zbl 0215.17601
[9] Lafata, P., Rosen, J. B.: An interactive display for approximation by linear programming. C.A.C.M.13, 651–659 (1970). · Zbl 0217.22504
[10] Rabinowitz, P.: Applications of linear programming to numerical analysis. SIAM Review10, 121–159 (1968). · Zbl 0236.65001 · doi:10.1137/1010029
[11] Theil, H., Van de Panne, C.: Quadratic programming as an extension of conventional quadratic maximization. Management Science7, 1–20 (1960). · Zbl 0995.90604 · doi:10.1287/mnsc.7.1.1
[12] Dierckx, P.: An algorithm for least-squares cubic spline fitting with convexity and concavity constraints. Applied Mathematics and Programming Division Report TW 39, K. U. Leuven, 1978.
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