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.
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