The course will discuss the theory and practice of approximation of functions and data, in both the univariate and multivariate setting, with an emphasis on splines of various types and interpolation. A part of the course will be held in a Laboratory setting where some of the techniques presented during the lectures will be implemented in Matlab. At the end of the course the student is expected to able to demonstrate an in-depth knowledge of the techniques of univariate and multivariate approximation.
Peano Kernel formula
Univariate splines of degrees 0, 1 and 3.
Cubic Smoothing splines
Subdivision of spline curves and surfaces
General Univariate Spline spaces
Thin Plate Splines in 2 dimensions
RBF interpolation and positive definite functions
The Theorems of Bochner, Schoenberg and Micchelli
|C. de Boor||A Practical Guide to Splines (Edizione 1)||Springer||1978|
|L. Bos||Course Notes||2017|
The purpose of the exam is to see if the student is able to recall and reproduce the theory and practice of interpolation and approximation, both univariate and multivariate. The exam will be oral.
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