Mathematics Colloquia and Seminars

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Splines, were introduced as interpolation tools as early as in the first half of the 19th Century by Lobachevsky (Hyperbolic Geometry) and 'rediscovered' by Forrest and Schoenberg in the mid-20th Century motivated by problems arising in the design of ship hulls and air wings; the variational theory of splines, originated with the work of Holliday, Laurent, Atteia, Anselone. Epi-splines, spline-like functions, were used for the first time as approximation tools rather recently (2002) motivated originally by the design of financial curves and then later, by a wide variety of applications. In this lecture, I shall provide a short history of this development and sketch out the accompanying evolving theory that relies to a large extent on Variational Analysis.