Convergence Rates for Greedy Algorithms in Reduced Basis Methods

By Peter Binev, Albert Cohen, Wolfgang Dahmen, Ronald A. DeVore, Guergana Petrova, Przemyslaw Wojtaszczyk. SIAM Journal on Mathematical Analysis, 2010

484 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1ec2c921b690d2f1f13586994dc51083b8a02dd3

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Citations in the corpus

A Stochastic Collocation Algorithm with Multifidelity Models (2014, background): “to the manifold u(Γ) that, as N increases, decays commensurately with the N -width [1, 5].”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, background): “, diffusiondominated problems), employing a linear trial subspace is theoretically justifiable [3, 6] and has enjoyed many successful demonstrations.”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “The application of greedy algorithms to optimization in tensor formats was rigorously studied in [12, 2, 26].”
Stabilized reduced basis method for parametrized advection-diffusion PDEs (2014, background): “Several options have been recently proposed to improve the sampling strategy [11, 13] For further details about the convergence rates of this algorithm, we refer to [2].”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, result): “In the case that one is able to obtain exponential convergence in the n-width, that is to say dn(M;X)≤C exp(−αnβ ) for some constants C,α,β > 0, exponential convergence is also inherited (albeit at a reduced rate) by reduced-order approximations, and the same equivalence holds also for algebraic con”
Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, methodology): “As such reduced grid-based methods, we would like to mention the sparse grids technique [13], as well as the initial tensor-structured approaches: the greedy algorithm in the canonical tensor format [14, 15, 16, 17, 18], and the solver in the Tucker format, based on the manifold dynamics via the pro”
Evaluation of aerodynamic loads via reduced order methodology (2015, unknown): “[23], as well as in [31].”