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2012

Greedy Algorithms for Reduced Bases in Banach Spaces

DeVore, Ronald, Petrova, Guergana, Wojtaszczyk, Przemyslaw

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Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n dimensional space X_n \subset X which can be used to approximate the elements of F.

The best possible error we can achieve for such an approximation is given by the Kolmogorov width d_n(F)_X.
However, finding the space which gives this performance is typically numerically intractable.
Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs.

Greedy Algorithms for Reduced Bases in Banach Spaces · Around

Built on

E. Hewitt, K. Stromberg, Real and Abstract Analysis
1969
Earlier work this paper cites.
G.G. Lorentz, M. von Golitschek, and Y. Makovoz, Constructive Approximation: Advanced Problems
1996
Earlier work this paper cites.

Similar

Y. Maday, A.T. Patera, and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parametric elliptic partial differential equations
2002
Cited alongside, same era.
Y. Maday, A. T. Patera, and G. Turinici, Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
2002
Cited alongside, same era.

Then

P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced bases
2011
Later among the works it cites.
A. Buffa, Y. Maday, A.T. Patera, C. Prud’homme, and G. Turinici, A Priori convergence of the greedy algorithm for the parameterized reduced basis
2012
Closest in time.

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