Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T10:34:48.109Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of methods for tabular interpolation

Published online by Cambridge University Press:  24 October 2008

F. M. Larkin
F. M. Larkin
Affiliation:
Culham Laboratory (U.K.A.E.A.)
Get access Rights & Permissions [Opens in a new window]

Abstract

A generalization of the Neville–Aitken method is described which allows the construction of interpolating functions, other than polynomials, by means of simple recurrence relations. In particular, simple constructions are given for rational functions and trigonometric series which interpolate prescribed function values at non-equispaced positions of the independent variable.

Restrictions imposed by requiring the interpolating functions to be invariant under linear transformations of the coordinates are discussed, and application of the technique to the problem of inverse interpolation is also considered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1101 - 1114
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hildebrand, F. B.Introduction to numerical analysis (McGraw-Hill, 1956).Google Scholar
(2)Larkin, F. M.Some techniques for rational interpolation. Computer J. 10, No. 2 (1967).CrossRefGoogle Scholar
(3)Neville, E. H.J. Indian Math. Soc. 20 (1934), 87–120.Google Scholar
(4)Ostrowski, A. M.Solution of equations and systems of equations, Chap. 13 (Academic Press: N.Y. and London, 1960).Google Scholar
(5)Stoer, J.Alogrithmen zur Interpolation mit rationalen Funktionen, Numer. Math. 3 (1961), 285–304.CrossRefGoogle Scholar
(6)Thiele, T. N.Interpolationsrechnung, Teubner, B. C. (Leipzig, 1909).Google Scholar