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Mathematics of Computation

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Interpolation by convex quadratic splines


Authors: David F. McAllister and John A. Roulier
Journal: Math. Comp. 32 (1978), 1154-1162
MSC: Primary 41A05; Secondary 41A15
DOI: https://doi.org/10.1090/S0025-5718-1978-0481734-6
MathSciNet review: 0481734
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Abstract: Algorithms are presented for computing a quadratic spline interpolant with variable knots which preserves the monotonicity and convexity of the data. It is also shown that such a spline may not exist for fixed knots.


References [Enhancements On Off] (What's this?)

  • [1] CARL de BOOR, A Practical Guide to Splines, Springer-Verlag, Berlin and New York. (To appear.) MR 804666 (86h:65015)
  • [2] R. PETER DUBE, "Univariate blending functions and alternatives," Comput. Graphics and Image Processing, v. 6, 1977, pp. 394-408.
  • [3] R. PETER DUBE, "Automatic generation of parameters for preliminary interactive design of free-form curves." (To appear.)
  • [4] G. G. LORENTZ, Approximation of Functions, Holt, Rinehart and Winston, New York, 1966. MR 0213785 (35:4642)
  • [5] D. F. McALLISTER, E. PASSOW & J. A. ROULIER, "Algorithms for computing shape preserving spline interpolations to data," Math. Comp., v. 31, 1977, pp. 717-725. MR 0448805 (56:7110)
  • [6] E. PASSOW & J. A. ROULIER, "Monotone and convex spline interpolation," SIAM J. Numer. Anal., v. 14, 1977, pp. 904-909. MR 0470566 (57:10316)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0481734-6
Article copyright: © Copyright 1978 American Mathematical Society

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