Free Access
Volume 48, Number 6, November-December 2014
Page(s) 1777 - 1806
Published online 03 October 2014
  1. A. Ammar, B. Mokdad, F. Chinesta and R. Keunings, 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. [CrossRef] [Google Scholar]
  2. A. Ammar, F. Chinesta and A. Falco, On the convergence of a greedy rank-one update algorithm for a class of linear systems. Arch. Comput. Methods Engrg. 17 (2010) 473–486. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  4. J. Ballani and L. Grasedyck, A projection method to solve linear systems in tensor format. Numer. Linear Algebra Appl. 20 (2013) 27-43. [CrossRef] [MathSciNet] [Google Scholar]
  5. G. Beylkin and M.J. Mohlenkamp, Algorithms for numerical analysis in high dimensions. SIAM J. Sci. Comput. 26 (2005) 2133–2159. [CrossRef] [Google Scholar]
  6. E. Cances, V. Ehrlacher and T. Lelievre, Convergence of a greedy algorithm for high-dimensional convex nonlinear problems. Math. Models Methods Appl. Sci. 21 (2011) 2433–2467. [Google Scholar]
  7. E. Cances, V. Ehrlacher and T. Lelievre, Greedy algorithms for high-dimensional non-symmetric linear problems (2012). Preprint: arXiv:1210.6688v1. [Google Scholar]
  8. A. Cohen, W. Dahmen and G. Welper, Adaptivity and variational stabilization for convection-diffusion equations. ESAIM: M2AN 46 (2012) 1247–1273. [CrossRef] [EDP Sciences] [Google Scholar]
  9. F. Chinesta, P. Ladeveze and E. Cueto, A short review on model order reduction based on proper generalized decomposition. Arch. Comput. Methods Engrg. 18 (2011) 395–404. [Google Scholar]
  10. W. Dahmen, C. Huang, C. Schwab and G. Welper, Adaptive petrov–galerkin methods for first order transport equations. SIAM J. Numer. Anal. 50 (2012) 2420–2445. [CrossRef] [Google Scholar]
  11. L. De Lathauwer, B. De Moor and J. Vandewalle, A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21 (2000) 1253–1278. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Doostan and G. Iaccarino, A least-squares approximation of partial differential equations with high-dimensional random inputs. J. Comput. Phys. 228 (2009) 4332–4345. [CrossRef] [Google Scholar]
  13. A. Ern and J.-L. Guermond, Theory and practice of finite elements. Vol. 159 of Appl. Math. Sci. (2004). [Google Scholar]
  14. M. Espig and W. Hackbusch, A regularized newton method for the efficient approximation of tensors represented in the canonical tensor format. Numer. Math. 122 (2012) 489–525. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Falcó and A. Nouy, A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach. J. Math. Anal. Appl. 376 (2011) 469–480. [CrossRef] [Google Scholar]
  16. A. Falcó and W. Hackbusch, On minimal subspaces in tensor representations. Found. Comput. Math. 12 (2012) 765–803. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Falcó and A. Nouy, Proper generalized decomposition for nonlinear convex problems in tensor banach spaces. Numer. Math. 121 (2012) 503–530. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Falcó, W. Hackbusch and A. Nouy, Geometric structures in tensor representations. Preprint 9/2013, MPI MIS. [Google Scholar]
  19. L. Figueroa and E. Suli, Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators. Found. Comput. Math. 12 (2012) 573–623. [Google Scholar]
  20. L. Giraldi, Contributions aux Méthodes de Calcul Basées sur l’Approximation de Tenseurs et Applications en Mécanique Numérique. Ph.D. thesis, École Centrale Nantes (2012). [Google Scholar]
  21. L. Giraldi, A. Nouy, G. Legrain and P. Cartraud, Tensor-based methods for numerical homogenization from high-resolution images. Comput. Methods Appl. Mech. Engrg. 254 (2013) 154–169. [CrossRef] [MathSciNet] [Google Scholar]
  22. L. Grasedyck, Hierarchical singular value decomposition of tensors. SIAM J. Matrix Anal. Appl. 31 (2010) 2029–2054. [CrossRef] [Google Scholar]
  23. L. Grasedyck, D. Kressner and C. Tobler, A literature survey of low-rank tensor approximation techniques. GAMM-Mitteilungen 36 (2013) 53–78. [CrossRef] [MathSciNet] [Google Scholar]
  24. W. Hackbusch, Tensor Spaces and Numerical Tensor Calculus. In vol. 42 of Springer Series in Computational Mathematics (2012). [Google Scholar]
  25. W. Hackbusch and S. Kuhn, A New Scheme for the Tensor Representation. J. Fourier Anal. Appl. 15 (2009) 706–722. [CrossRef] [MathSciNet] [Google Scholar]
  26. S. Holtz, T. Rohwedder and R. Schneider, The Alternating Linear Scheme for Tensor Optimisation in the TT format. SIAM J. Sci. Comput. 34 (2012) 683–713. [CrossRef] [Google Scholar]
  27. S. Holtz, T. Rohwedder and R. Schneider, On manifolds of tensors with fixed TT rank. Numer. Math. 120 (2012) 701–731. [CrossRef] [MathSciNet] [Google Scholar]
  28. B.N. Khoromskij and C. Schwab, Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. SIAM J. Sci. Comput. 33 (2011) 364–385. [CrossRef] [Google Scholar]
  29. B.N. Khoromskij, Tensors-structured numerical methods in scientific computing: Survey on recent advances. Chemometrics and Intelligent Laboratory Systems 110 (2012) 1–19. [Google Scholar]
  30. T.G. Kolda and B.W. Bader, Tensor decompositions and applications. SIAM Review 51 (2009) 455–500. [Google Scholar]
  31. D. Kressner and C. Tobler, Low-rank tensor krylov subspace methods for parametrized linear systems. SIAM J. Matrix Anal. Appl. 32 (2011) 1288–1316. [CrossRef] [MathSciNet] [Google Scholar]
  32. P. Ladevèze, Nonlinear Computational Structural Mechanics - New Approaches and Non-Incremental Methods of Calculation. Springer Verlag (1999). [Google Scholar]
  33. P. Ladevèze, J.C. Passieux and D. Néron, The LATIN multiscale computational method and the Proper Generalized Decomposition. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1287–1296. [Google Scholar]
  34. H. G. Matthies and E. Zander, Solving stochastic systems with low-rank tensor compression. Linear Algebra Appl. 436 (2012). [Google Scholar]
  35. A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Comput. Methods Appl. Mech. Engrg. 196 (2007) 4521-4537. [CrossRef] [MathSciNet] [Google Scholar]
  36. A. Nouy, Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations, Arch. Comput. Methods Engrg. 16 (2009) 251–285. [Google Scholar]
  37. A. Nouy, Proper Generalized Decompositions and separated representations for the numerical solution of high dimensional stochastic problems. Arch. Comput. Methods Engrg. 17 (2010) 403–434. [CrossRef] [Google Scholar]
  38. A. Nouy, A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1603–1626. [Google Scholar]
  39. I.V. Oseledets and E.E. Tyrtyshnikov, Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput. 31 (2009) 3744–3759. [Google Scholar]
  40. I.V. Oseledets, Tensor-train decomposition. SIAM J. Sci. Comput. 33 (2011) 2295–2317. [CrossRef] [MathSciNet] [Google Scholar]
  41. T. Rohwedder and A. Uschmajew, On local convergence of alternating schemes for optimization of convex problems in the tensor train format. SIAM J. Numer. Anal. 51 (2013) 1134–1162. [CrossRef] [Google Scholar]
  42. V. Temlyakov, Greedy Approximation. Camb. Monogr. Appl. Comput. Math. Cambridge University Press (2011). [Google Scholar]
  43. V. Temlyakov, Greedy approximation. Acta Numerica 17 (2008) 235–409. [Google Scholar]
  44. A. Uschmajew and B. Vandereycken, The geometry of algorithms using hierarchical tensors. Technical report, ANCHP-MATHICSE, Mathematics Section, EPFL (2012). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you