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Manuscript Title: Routines for numerical interpolation, with first and second order differentiation, having non-uniformly spaced points, out to three dimensions.
Authors: J. Waite
Program title: LNIDIF
Catalogue identifier: AAXJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 46(1987)323
Programming language: Fortran.
Computer: PERKIN-ELEMER 3240.
RAM: 23K words
Word size: 32
Keywords: General purpose, Interpolation, Lagrangian polynomials, Numerical Differentiation with Non-uniform spacing.
Classification: 4.10.

Nature of problem:
Interpolates and calculates the first and second derivatives of any function defined by a series of points out to three dimensions.

Solution method:
An (N-1)-th order Lagrangian polynomial is fitted to the N points for interpolation, which (N-2) and (N-3) ordered polynomials are used for the 1st and 2nd derivatives respectively.

Restrictions:
The submitted version of the test MAIN segment is set to a maximum of 10 points per dimension and can be readily upgraded. It is also proposed that generalisation to M dimensions (>3) and/or higher derivatives can readily be implemented.

Unusual features:
The access of the function values, in the routines, is vectorised for transportability and efficiency.

Running time:
0.05 * N * M seconds (N points, M dimensions)