How do you build a smooth convex interpolant?

Yves Lucet
University of Victoria/Mathematics and Statistics
lucet@na-net.ornl.gov

ABSTRACT. Assume you know the values of a smooth convex function and of its gradient on a grid. We propose to build a smooth convex interpolatory function by computing a convex piecewise-linear function whose Moreau envelope interpolates the given points.

One of our motivations for looking at convex interpolatory algorithms comes from computing fast transforms: the Fast Legendre Transform and the Fast Moreau Envelope always return a grid of values. Instead of returning a piecewise-linear function, the above algorithm returns a smooth convex function which is usually more visually pleasing.

(Back to main WCOM page.)