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Manuscript Title: Newton-Everett interpolation of continuous functions.
Authors: J.A. Hernando
Program title: FINT
Catalogue identifier: AARS_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 27(1982)73
Programming language: Fortran.
Computer: IBM 370/158.
Operating system: OS/VS1 OR VM370/CMS.
RAM: 234K words
Word size: 32
Keywords: General purpose, Newton, Interpolation, Everett interpolation, Finite differences, Continuous approximation.
Classification: 4.10.

Nature of problem:
Interpolation needs are deeply rooted in almost all branches of physics because of the uncommonness of analytical solutions and the discrete nature of physical measurements.

Solution method:
If the calculations one is doing are very time consuming, it would be convenient to minimize these calculations and to interpolate whenever possible. In this paper we describe an interpolation routine that employs the finite difference formulae of Newton and Everett. The routine is designed to work with a continuous function defined on an evenly spaced set of points. The main purpose is to do the calculations in a quick and accurate form. The calculation is divided into two parts:
i) a calculation which depends exclusively on the points where the function is given and on the accuracy requested;
ii) a calculation dependent on the point where one wishes to interpolate.
The first calculations are done only once and are then available for the following calculations.

In the program it is assumed that the set of points where the function is defined is less than or equal to 200. This can be easily changed. If the function to be interpolated has a pathological behaviour, the results are strongly dependent on the size of the separation between functional values, so special care must be taken with this point.

Running time:
The average running time depends on the number of interpolation points calculated. However, it can be estimated to be of the order of 3 times that needed for a double-precision expotential.