A simple method for monotonic interpolation in one dimension.
Abstract
A simple method is proposed for a 1dimensional interpolation on a given set of data points (x_{i}, y_{i}). In each interval (x_{i},, X_{i+1}) the interpolation function is assumed to be a third order polynomial passing through the data points. The slope at each grid point is determined in such a way as to guarantee a monotonic behavior of the interpolating function. The result is a smooth curve with continuous firstorder derivatives that passes through any given set of data points without spurious oscillations. Local extrema can occur only at grid points where they are given by the data, but not in between two adjacent grid points. The method gives exact results if the data points correspond to a secondorder polynomial.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1990
 Bibcode:
 1990A&A...239..443S
 Keywords:

 numerical methods;
 interpolation;
 hydrodynamics