FUNCOMP · Numerical Computation with Functions Instead of Numbers

Numerical analysis, scientific computing, and computational science are built on technologies of discretization such as splines, finite differences, and finite elements. Yet for most applications it is ultimately continuous functions that are of scientific interest, and the discretizations are a means to the end of working with them. This project will advance mathematics and algorithms to enable scientists and engineers to compute with functions rather than their discretizations. Such computations will be numerical as opposed to symbolic, for speed and wide applicability, yet will achieve some of the “feel” of symbolic computing. The goal is to do for computing with functions what floating-point arithmetic has done for computing with numbers: to hide away details of discretization from most users, most of the time.""