On the Convergence of a Greedy Rank-One Update Algorithm for a Class of Linear Systems

Archives of Computational Methods in Engineering

Volumn 17, Issue 4, 2010, Pages 473-486

  Ammar, A ^a   Chinesta, F ^b   Falco A ^c  

^a ARTS ET MÉTIERS PARISTECH   (France)

^b INSTITUT DE RECHERCHE EN GÉNIE CIVIL ET MÉCANIQUE GEM   (France)

^c UNIVERSIDAD CEU CARDENAL HERRERA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE ANALYSIS; DIRICHLET BOUNDARY CONDITION; HIGH-DIMENSIONAL; MODEL PROBLEMS; NUMERICAL EXAMPLE; SERIES SOLUTIONS; TENSORIAL PRODUCTS;

APPROXIMATION ALGORITHMS; BOUNDARY CONDITIONS; DIFFERENTIATION (CALCULUS); FINITE ELEMENT METHOD; LINEAR SYSTEMS; POISSON EQUATION;

CONVERGENCE OF NUMERICAL METHODS;

EID: 78549238137     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11831-010-9048-z     Document Type: Article

References (16)

1. Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in Kinetic Theory modelling Complex Fluids. J Non-Newton Fluid Mech 139: 153-176.
2. Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in Kinetic Theory modelling Complex Fluids. Part II: Transient simulations using space-time separated representations. J Non-Newton Fluid Mech 144: 98-121.
3. Beylkin G, Mohlenkamp MJ (2005) Algorithms for numerical analysis in high dimensions. SIAM J Sci Comput 26(6): 2133-2159.
4. de Silva V, Lim L-H (2008) Tensor Rank and Ill-posedness of the best low-rank approximation problem. SIAM J Matrix Anal Appl 30(3): 1084-1127.
5. Graham A (1981) Kronecker products and matrix calculus with applications. Wiley, New York.
6. Grasdyck L (2004) Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure. Computing 72: 247-265.
7. Friedman JH, Stuezle W (1981) Projection pursuit regression. J Am Statist Assoc 76: 817-823.
8. Huber PJ (1985) Projection pursuit. Ann Statist 13(2): 435-475.
9. Kolda T (2001) Orthogonal tensor decompositions. SIAM J Matrix Anal Appl 20(1): 243-255.
10. de Lathauwer L, de Moor B, Vandewalle J (2000) A multilinear singular value decomposition. SIAM J Matrix Anal Appl 21(4): 1253-1278.
11. N) approximations of high order tensors. SIAM J Matrix Anal Appl 21(4): 1324-1342.
12. Mallat S, Zhang Z (1993) Matching pursuit with time-frequency dictionaries. IEEE Trans Signal Process 41: 3397-3415.
13. Ruszczyński A (2006) Nonlinear optimization. Princeton University Press, Princeton.
14. N Temlyakov V (2008) Greedy approximation. Acta Numer, pp 235-409.
15. van Loan CF (2000) The ubiquitous Kronecker product. J Comput Appl Math 123: 85-100.
16. Zhang T, Golub G (2000) Rank-one approximation to high order tensors. SIAM J Matrix Anal Appl 21(4): 1253-1278.