Algorithms for computing shape preserving spline interpolations to data

McAllister, David F.; Passow, Eli; Roulier, John A.

doi:10.1090/S0025-5718-1977-0448805-0

Algorithms for computing shape preserving spline interpolations to data
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by David F. McAllister, Eli Passow and John A. Roulier PDF

Math. Comp. 31 (1977), 717-725 Request permission

Abstract:

Algorithms are presented for computing a smooth piecewise polynomial interpolation which preserves the monotonicity and/or convexity of the data.

References

Robert E. Barnhill and Richard F. Riesenfeld (eds.), Computer aided geometric design, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0349061
Wayne T. Ford and John A. Roulier, On interpolation and approximation by polynomials with monotone derivatives, J. Approximation Theory 10 (1974), 123–130. MR 350259, DOI 10.1016/0021-9045(74)90111-7
A. R. Forrest, Interactive interpolation and approximation by Bézier polynomials, Comput. J. 15 (1972), 71–79. MR 315866, DOI 10.1016/0010-4485(90)90038-E
William J. Gordon and Richard F. Riesenfeld, Bernstein-Bézier methods for the computer-aided design of free-form curves and surfaces, J. Assoc. Comput. Mach. 21 (1974), 293–310. MR 353625, DOI 10.1145/321812.321824
William J. Kammerer, Polynomial approximations to finitely oscillating functions, Math. Comp. 15 (1961), 115–119. MR 123865, DOI 10.1090/S0025-5718-1961-0123865-3
G. G. Lorentz, Bernstein polynomials, Mathematical Expositions, No. 8, University of Toronto Press, Toronto, 1953. MR 0057370
Eli Passow, Piecewise monotone spline interpolation, J. Approximation Theory 12 (1974), 240–241. MR 361544, DOI 10.1016/0021-9045(74)90066-5
Eli Passow, An improved estimate of the degree of monotone interpolation, J. Approximation Theory 17 (1976), no. 2, 115–118. MR 417624, DOI 10.1016/0021-9045(76)90032-0
Eli Passow, Monotone quadratic spline interpolation, J. Approximation Theory 19 (1977), no. 2, 143–147. MR 440246, DOI 10.1016/0021-9045(77)90036-3
Eli Passow and Louis Raymon, The degree of piecewise monotone interpolation, Proc. Amer. Math. Soc. 48 (1975), 409–412. MR 430608, DOI 10.1090/S0002-9939-1975-0430608-4
Eli Passow and John A. Roulier, Monotone and convex spline interpolation, SIAM J. Numer. Anal. 14 (1977), no. 5, 904–909. MR 470566, DOI 10.1137/0714060
Steven Pruess, Properties of splines in tension, J. Approximation Theory 17 (1976), no. 1, 86–96. MR 407491, DOI 10.1016/0021-9045(76)90113-1
Zalman Rubinstein, On polynomial $\delta$-type functions and approximation by monotonic polynomials, J. Approximation Theory 3 (1970), 1–6. MR 261228, DOI 10.1016/0021-9045(70)90057-2
H. Späth, Exponential spline interpolation, Computing (Arch. Elektron. Rechnen) 4 (1969), 225–233 (English, with German summary). MR 248966, DOI 10.1007/bf02234771
W. Wolibner, Sur un polynôme d’interpolation, Colloq. Math. 2 (1951), 136–137 (French). MR 43946, DOI 10.4064/cm-2-2-136-137
Sam W. Young, Piecewise monotone polynomial interpolation, Bull. Amer. Math. Soc. 73 (1967), 642–643. MR 212455, DOI 10.1090/S0002-9904-1967-11806-8