Piecewise-linear approximation to continuous functions

Abstract

Methods are examined for finding an optimal least-squares approximation to a continuous function on a finite interval by a continuous piecewise-linear function with a specified number of linear segments. A practical method and a corresponding computer program are presented which use the solution of the simpler problem where the approximating function is not constrained to be continuous. The topic arises in connection with the use of diode function generators to represent functions on an analogue computer.