A Simple Method for Monotonic Interpolation in One Dimension

Details A Simple Method for Monotonic Interpolation in One Dimension A Simple Method for Monotonic Interpolation in One Dimension

Nov 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990a%26a...239..443s&link_type=abstract

Astronomy and Astrophysics, Vol. 239, NO. NOV(II), P. 443, 1990

Astronomy and Astrophysics

Astrophysics

28

Numerical Methods, Interpolation, Hydrodynamics

Scientific paper

A simple method is proposed for a 1-dimensional interpolation on a given set of data points (xi, yi). In each interval (xi,, Xi+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 first-order 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 second-order polynomial.

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