Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT-format

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 26, Issue 5, 2011, Pages 465-489

  Lebedeva, O S ^a,b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE RATES; EIGENVALUES; MATHEMATICAL PHYSICS; NUMERICAL EXPERIMENTS; OPTIMIZATION PROBLEMS; RAYLEIGH QUOTIENTS; SPECTRAL PROBLEM; SYMMETRIC MATRICES; TENSOR METHOD; TENSOR REPRESENTATION; WORKING TIME;

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; TENSORS;

CONJUGATE GRADIENT METHOD;

EID: 81355160934     PISSN: 09276467     EISSN: 15693988     Source Type: Journal    
DOI: 10.1515/RJNAMM.2011.026     Document Type: Article

References (15)

1. E. G. D'yakonov and A. V. Knyazev. A group iterationmethod for finding the lowest eigenvalues. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., (2):29-34, 81, 1982.
2. M. Espig. Effiziente Bestapproximation mittels Summen von Elementartensoren in hohen Dimensionen. PhD thesis, Universität Leipzig, Leipzig, 2008.
3. W. Hackbusch, B.N. Khoromskij, and E. E. Tyrtyshnikov. Approximate iterations for structured matrices. Numer. Math. ( 2008) 109, No. 3, 365-383.
4. V.A. Kazeev and B.N. Khoromskij. On explicit QTT representations of Laplace operator and its inverse. Preprint 2010-75, MPI MIS, Leipzig, 2010.
5. B. Khoromskij and I. Oseledets. DMRG+QTT approach to high-dimensional quantum molecular dynamics. Preprint 2010-69, MPI MIS, Leipzig, 2010.
6. A.V. Knyazev. Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comput. (2001) 23, No. 2, 517-541.
7. O.S. Lebedeva. Block tensor conjugate gradient-type method for Rayleigh quotient minimization in two-dimensional case. Comp. Math. Math. Phys. (2010) 50, No. 5, 749-765.
8. M. Nest and H.D.Meyer. Benchmark calculations on high-dimensional Henon-Heiles potentials with the multi-configuration time dependent Hartree (MCTDH) method. Chem. Phys. (2002) 117, 10499.
9. I. V. Oseledets. Approximation of 2d ×2d Matrices Using Tensor Decomposition. SIAM J. Matrix Anal. Appl. (2010) 31, 2130.
10. I. V. Oseledets. Explicit tensor-train representation of certain functions. Preprint 2010-04, INM RAS, Moscow, 2010.
11. I. V. Oseledets and E. E. Tyrtyshnikov. Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comp. (2009) 31, No. 5, 3744-3759.
12. I.V. Oseledets. A new tensor decomposition. Doklady Math. (2009) 80, 495-496.
13. I.V. Oseledets and E.E. Tyrtyshnikov. Recursive decomposition of multidimensional tensors. Doklady Math. (2009) 80, 460-462.
14. I.V. Oseledets and E.E. Tyrtyshnikov. TT-cross approximation for multidimensional arrays. Lin. Algebra Appl. (2010) 432, No. 1, 70-88.
15. I.V. Oseledets S.A. Goreinov and D.V. Savostyanov. Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case. Preprint 2010-01, INM RAS, 2010.