**Greedy Algorithms for Generating Reduced Bases**

Parametric PDEs arise in design and control problems and also when solving stochastic PDEs. They pose a numerical challenge when the number of parameters is large. This has driven the development of many innovative numerical techniques. One of these is the so-called â€™reduced basis methodâ€™ whose goal is to find a small number of parameters such that the solutions for these parameters span a good Galerkin subspace which can be used to approximate the solution for any parameter selection. One often used strategy for find such a reduced basis is a greedy algorithm which can be formulated as an approximation strategy in any Hilbert space. We shall discuss the interesting history about what is known about convergence rates for this algorithm. This represents joint work with Peter Binev, Albert Cohen, Wolfgang Dahmen, Guergana Petrova, and Przemek Wojtaszczyk.

Aachen Institute for Advanced Study in Computational Engineering Science
(AICES) |