13 research outputs found
Two ways to generate monotonic sequences:Convexity and ratios
Here we give an account of two appealingly simple techniques to generate monotonic sequences that were developed by the author and Grahame Bennett. Sadly, Bennett died in 2016 after a lifetime of distinguished contributions in the field of inequalities. This article is dedicated to him
Error estimates for interpolation of rough data using the scattered shifts of a radial basis function
The error between appropriately smooth functions and their radial basis
function interpolants, as the interpolation points fill out a bounded domain in
R^d, is a well studied artifact. In all of these cases, the analysis takes
place in a natural function space dictated by the choice of radial basis
function -- the native space. The native space contains functions possessing a
certain amount of smoothness. This paper establishes error estimates when the
function being interpolated is conspicuously rough.Comment: 12 page
Variational methods in convex analysis
We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory