A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems-Reference-Cited by-同舟云学术

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

Published:2014-10-03 Issue:6 Volume:48 Page:1777-1806
ISSN:0764-583X
Container-title:ESAIM: Mathematical Modelling and Numerical Analysis
language:
Short-container-title:ESAIM: M2AN

Author:

Billaud-Friess M.,Nouy A.,Zahm O.

Publisher

EDP Sciences

Subject

Applied Mathematics,Modelling and Simulation,Numerical Analysis,Analysis,Computational Mathematics

Link

http://www.esaim-m2an.org/10.1051/m2an/2014019/pdf

Reference44 articles.

1. Ammar A., Mokdad B., Chinesta F. and Keunings R., A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids.J. Non-Newtonian Fluid Mech.139(2006) 153–176.

2. Ammar A., Chinesta F. and Falco A., On the convergence of a greedy rank-one update algorithm for a class of linear systems.Arch. Comput. Methods Engrg.17(2010) 473–486.

3. M. Bachmayr and W. Dahmen, Adaptive near-optimal rank tensor approximation for high-dimensional operator equations.Found. Comput. Math.(2014) DOI:10.1007/s10208-013-9187-3.

4. Ballani J. and Grasedyck L., A projection method to solve linear systems in tensor format.Numer. Linear Algebra Appl.20(2013) 27-43.

5. Beylkin G. and Mohlenkamp M.J., Algorithms for numerical analysis in high dimensions.SIAM J. Sci. Comput.26(2005) 2133–2159.

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