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On Interpolation by Iteration of Proportional Parts, without the Use of Differences

Published online by Cambridge University Press:  20 January 2009

A. C. Aitken
A. C. Aitken
Affiliation:
Edinburgh University.
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Linear interpolation between two values of a function ua and ub can be performed, as is well known, in either of two ways. If the divided difference (ub−ua)/(b−a), which is usually denoted by u (a, b) or u (b, a), is provided, or its equivalent in tables at unit interval (the ordinary difference), we should generally prefer to use the formula

which is the linear case of Newton's fundamental formula for interpolation by divided differences. If differences are not given, but a machine is available, then the use of proportional parts in the form of the weighted average

the linear case of Lagrange's formula, is actually more convenient, since it involves no clearing of the product dials until the final result is read.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 1 , March 1932 , pp. 56 - 76
Copyright
Copyright © Edinburgh Mathematical Society 1932

References

page 57 note 1 For investigations of Jordan's formula, and of an allied formula suggested by the present writer where an odd number of tabular values are used, see articles in the Mathematical Gazette, 16 (1932), 14–25.CrossRefGoogle Scholar

page 72 note 1 It is advisable to do the work well to the left of the machine, in order to leave room for the division process, the divisor having several digits.Google Scholar