Rounded Approximate Step Functions For Interpolation

Abstract

Rounded approximate step functions of form x(Sup m)/(x(Sup n) + 1) and 1/(x(Sup n) + 1) useful in interpolating between local steep slopes or abrupt changes in tabulated data varying more smoothly elsewhere. Used instead of polynomial curve fits. Interpolation formulas based on these functions implemented quickly and easily on computers. Used in real-time control computations to interpolate between tabulated data governing control responses.