scholarly journals Convergence Rates for Greedy Algorithms in Reduced Basis Methods

2011 ◽  
Vol 43 (3) ◽  
pp. 1457-1472 ◽  
Author(s):  
Peter Binev ◽  
Albert Cohen ◽  
Wolfgang Dahmen ◽  
Ronald DeVore ◽  
Guergana Petrova ◽  
...  

2010 ◽  
Author(s):  
Peter Binev ◽  
Albert Cohen ◽  
Wolfgang Dahmen ◽  
Ronald DeVore ◽  
Guergana Petrova ◽  
...  


2014 ◽  
Vol 48 (3) ◽  
pp. 623-663 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Christian Plesken ◽  
Gerrit Welper


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tobias Danczul ◽  
Clemens Hofreither

Abstract We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In particular, we demonstrate that several recently proposed RBMs for fractional diffusion can be interpreted as RKMs. This changed point of view allows us to give convergence proofs for some methods where none were previously available. We also propose a new RKM for fractional diffusion problems with poles chosen using the best rational approximation of the function 𝑧 −𝑠 with 𝑧 ranging over the spectral interval of the spatial discretization matrix. We prove convergence rates for this method and demonstrate numerically that it is competitive with or superior to many methods from the reduced basis, rational Krylov, and direct rational approximation classes. We provide numerical tests for some elliptic fractional diffusion model problems.





2018 ◽  
Vol 6 (4) ◽  
pp. 1475-1502 ◽  
Author(s):  
Davide Torlo ◽  
Francesco Ballarin ◽  
Gianluigi Rozza


AIAA Journal ◽  
2002 ◽  
Vol 40 (8) ◽  
pp. 1653-1664 ◽  
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane


AIAA Journal ◽  
1993 ◽  
Vol 31 (9) ◽  
pp. 1712-1719 ◽  
Author(s):  
David M. McGowan ◽  
Susan W. Bostic


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