Alternatives to the exponential spline in tension
Author:
Steven Pruess
Journal:
Math. Comp. 33 (1979), 12731281
MSC:
Primary 65D07
MathSciNet review:
537971
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Abstract: A general setting is given for smooth interpolating splines depending on a parameter such that as this parameter approaches infinity the spline converges to the piecewise linear interpolant. The theory includes the standard exponential spline in tension, a rational spline, and several cubic splines. An algorithm is given for one of the cubics; the parameter for this example controls the spacing of new knots which are introduced.
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 W. GORDON & R. RIESENFELD, "Bspline curves and surfaces," in Computer Aided Geometric Design (Barnhill and Riesenfeld, Eds.), Academic Press, New York, 1974, pp. 95126. MR 0349061 (50:1555)
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 D. HILL, Estimation of Probability Functions Using Splines, Doctoral Thesis, Univ. of New Mexico, Albuquerque, 1973.
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 D. McALLISTER, E. PASSOW & J. ROULIER, "Algorithms for computing shape preserving spline interpolations to data," Math. Comp., v. 31, 1977, pp. 717725. MR 0448805 (56:7110)
 [9]
 G. NIELSON, "Some piecewise polynomial alternatives to splines under tension," in Computer Aided Geometric Design (Barnhill and Riesenfeld, Eds.), Academic Press, New York, 1974, pp. 209236. MR 0371012 (51:7235)
 [10]
 G. NIELSON, Unpublished notes, Dept. of Mathematics, Arizona State University.
 [11]
 E. PASSOW & J. ROULIER, "Monotone and convex spline interpolation," SIAM J. Numer. Anal., v. 14, 1977, pp. 904909. MR 0470566 (57:10316)
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 S. PRUESS, "Properties of splines in tension," J. Approximation Theory, v. 17, 1976, pp. 8696. MR 0407491 (53:11266)
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 D. SCHWEIKERT, "An interpolation curve using splines in tension," J. Math. and Phys., v. 45, 1966, pp. 312317. MR 0207174 (34:6990)
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 L. SHAMPINE & R. ALLEN, Numerical Computing, Saunders, Philadelphia, Pa., 1973. MR 0359250 (50:11705)
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 H. SPÄTH, "Exponential spline interpolation," Computing, v. 4, 1969, pp. 225233. MR 0248966 (40:2216)
 [16]
 H. SPÄTH, Spline Algorithms for Curves and Surfaces, Utilitas Mathematica Publ. Inc., Winnipeg, 1974. MR 0359267 (50:11722)
 [17]
 R. WIELINGA, "Constrained interpolation using Bézier curves," in Computer Aided Geometric Design (Barnhill and Riesenfeld, Eds.), Academic Press, New York, 1974, pp. 153172.
 [18]
 D. McALLISTER & J. ROULIER, "Interpolation by convex quadratic splines," Math. Comp., v. 32, 1978, pp. 11541162. MR 0481734 (58:1833)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905379716
PII:
S 00255718(1979)05379716
Article copyright:
© Copyright 1979
American Mathematical Society
