On smooth interpolation by continuously connected piecewise polynomials
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In this paper, a method is presented for interpolating to a given set of equally-spaced points a set of piecewise polynomials of degreen which agree in all derivatives throughn−1 at each of the points. Efficient computing algorithms and theorems, based on recursive difference equations and modern matrix techniques, are developed.
KeywordsSpline Function Spline Interpolation Mesh Point Polynomial Interpolation Interpolation Formula
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- D. T. Ross,General Description of the APT System, Servo-Mechanisms Laboratory, Mass. Inst. of Tech., vol. 1.Google Scholar
- T. N. E. Greville and I. J. Schoenberg,Smoothing by Generalized Spline Functions, SIAM National Meeting, New York, June 7, (1965).Google Scholar
- E. T. Whittaker and G. Robinson,The Calculus of Observations, London, Blackie and Son, 2nd Ed., (1937).Google Scholar
- Boris Podolsky,Curve Fitting With Allowance for Errors in Given Data, Technical Information Series No. R59 FPD 442, General Electric Company, Lockland, Ohio, July, (1959).Google Scholar
- J. F. Reilly,On Lidstone’s Demonstration of the Osculatory Interpolation Formula, The Record of the American Institute of Actuar., vol. XIV, Part. 1, Number 29, pp. 12–20, June, (1925).Google Scholar
- W. A. Jenkins,Osculatory Interpolation: New Derivation and Formulae, Record of the American Institute of Actuaries 15, pp. 87, (1926).Google Scholar
- I. J. Schoenberg,Spline Interpolation and the Higher Derivatives, Proc. Nat. Acad. Sci. U.S.A., pp. 24–28, (1964).Google Scholar
- C. Lanczos,Applied Analysis, Englewood Cliffs, Prentice Hall, Inc., p. 235, (1956).Google Scholar
- J. F. Price and R. H. Simonson,Various Methods and Computer Routines for Approximations, Curve Fittings, and Interpolation, Boeing Scientific Research Laboratories Document D1-82-0151, pp. 12–16, February, (1962).Google Scholar
- A. F. Cornock,The Numerical Solution of Poisson’s and the Bi-Harmonic Equations by Matrices, Proc. Cambridge Phil. Soc., vol. 50, (1954).Google Scholar