SSAF - Smooth spline approximations to functions.

Approximating a function accurately and reliably is a common problem arising in diverse fields: the design of circuits, the solution of partial differential equations, a cheap approximation to an expensive function, etc. Splines are a powerful and popular way to approximate functions. This paper presents an algorithm for obtaining nearly optimal spline approximations to functions over all possible orders and meshes. The technique is described, the software outline, a brief user's manual presented and many numerical results given showing the efficiency of the algorithm. The way in which the function is defined is immaterial to the algorithm used here: the function can be defined by a simple subroutine ( sin(x) ) or be unknown and defined only by a complex procedure such as the solution of a partial differential equation. All that is required is that the user be able to approximate the function with a spline of given order on a given mesh.