Solving discrete ill-posed problems with Tikhonov regularization and generalized cross validation

Kdy? 11.11.2010 13:00 - 14:30
Kde? ZČU / FAV / KMA / UL610 (učebna)
Kategorie

Gerard Meurant:  Solving discrete ill-posed problems with Tikhonov regularization and generalized cross validation

 

 

In this lecture we will show how to solve discrete ill--posed problems using Tikhonov regularization. The main problem is to find a meaningful regularization parameter. We will use generalized cross validation for that purpose. This amounts to find the minimum of a function involving quadratic forms  where  is a vector and  a rectangular matrix. Bounds for these quadratic forms will be obtained using the Golub-Kahan bidiagonalization algorithm which is based on the Lanczos process and Gauss quadrature. We will illustrate these techniques with examples arising from the discretization of integral equations and also with large difficult problems.

Přílohy

Evropská unie, ESF, MŠMT, OP Vzdělávání pro konkurenceschopnost, ZČU

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