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Mathematics of Computation

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A generalized interpolation algorithm

Author: A. C. R. Newbery
Journal: Math. Comp. 25 (1971), 549-552
MSC: Primary 65D05
MathSciNet review: 0312681
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Abstract: An interpolation algorithm is derived, which will construct an $ (n + 1)$-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.

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Keywords: Interpolation, osculatory interpolation, Bürmann series
Article copyright: © Copyright 1971 American Mathematical Society