Variation Diminishing Splines in Simulation

Abstract

Variation diminishing splines provide an effective tool for modeling active elements in circuit simulation. Using quadratic tensor product splines and maintaining uniform sampling at the boundary by linear extension of the data yields an algorithm that is smooth (unlike simple table lookup), shape preserving (unlike simple interpolation), and efficient (30 microseconds to evaluate on a Cray-IA). The rate of convergence to function and derivative values and to the location of minima is $O(h^2 )$.