The Theoretical Foundation of Reduced Basis Methods
نویسندگان
چکیده
The main theme of this volume is the efficient solution of families of stochastic or parametric partial differential equations. This article focuses on the theoretical underpinnings of such methods. It shows how concepts from approximation theory, such as entropy or widths, can help quantify a priori how well such methods can perform. This theory is then used to analyze one of the primary numerical vehicles, Reduced Basis Methods (RBMs), for parametric equations. A particular emphasis is placed on understanding the performance of greedy algorithms for selecting basis in RBMs.
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