Curve fitting by spline and akima methods: possibility of interpolation error and its suppression

Abstract

Two computer-implemented methods for achieving smooth interpolations between data points are compared with respect to their ability to avoid spurious oscillations. While both the spline and Akima interpolations may significantly overshoot the data points if the latter change abruptly, these phenomena can be suppressed or reduced in the Akima method by relatively minor modifications. The spline method cannot be similarly corrected, however, and its use is recommended only if the data points are sufficiently closely spaced in regions of rapidly changing slope.