A generalized interpolation algorithm
Abstract: An interpolation algorithm is derived, which will construct an -point interpolant based on any sequence of interpolatory functions that can be defined by a three-term linear recursion. By suitable parameter choice, a single algorithm can be made to interpolate in terms of the classical polynomial sequences or in terms of trigonometric or hyperbolic series etc. An analysis of truncation error is included.
-  A. C. R. Newbery, Interpolation by algebraic and trigonometric polynomials, Math. Comp. 20 (1966), 597–599. MR 0203905, https://doi.org/10.1090/S0025-5718-1966-0203905-8
-  F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR 0075670
-  J. Hart et al., Computer Approximations, Wiley, New York, 1968.
- A. C. R. Newbery, ``Interpolation by algebraic and trigonometric polynomials,'' Math. Comp., v. 20, 1966, pp. 597-599. MR 34 #3752. MR 0203905 (34:3752)
- F. B. Hildebrand, Introduction to Numerical Analysis, McGraw-Hill, New York, 1956. MR 17, 788. MR 0075670 (17:788d)
- J. Hart et al., Computer Approximations, Wiley, New York, 1968.
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Keywords: Interpolation, osculatory interpolation, Bürmann series
Article copyright: © Copyright 1971 American Mathematical Society