 |
B.N. Khoromskij, Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances. Preprint 21/2010, MPI MiS Leipzig 2010 (submitted).
|
|
B.N. Khoromskij, and I.V. Oseledets: Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs. Preprint MPI MIs, Leipzig 2010 (submitted).
|
|
S.V. Dolgov, B.N. Khoromskij, and E.E. Tyrtyshnikov: Tensor-Structured Solution of Elliptic Problems with Piecewise Smooth Coefficients. Leipzig/Moscow, 2010 (in preparation).
|
|
B.N. Khoromskij and Ch. Schwab: Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. Preprint MPI MiS 9/2010, Leipzig, 2010 (submitted).
|
|
B.N. Khoromskij, and I. V. Oseledets: Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions. Preprint 79/2009 MPI MiS, Leipzig 2009 (submitted).
|
|
T. Blesgen, V. Gavini and V. Khoromskaia: Tensor Product Approximation of the Electron Density of Large Aluminium Clusters in OFDFT. Preprint 66/2009 MPI MiS Leipzig, 2009.
|
|
B.N. Khoromskij: O(log N)-Quantics Approximation of N-d Tensors in High-Dimensional Numerical Modeling. Preprint 55/2009 MPI MiS, Leipzig 2009 (submitted).
|
|
B.N. Khoromskij, V. Khoromskaia, and H.-J. Flad: Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format. Preprint 44/2009 MPI MiS, Leipzig 2009 (SISC submitted).
|
|
B.N. Khoromskij: Tensor-structured Preconditioners and Approximate Inverse of Elliptic Operators in Rd. J. Constr. Approx., 30:599-620 (2009).
|
|
V. Khoromskaia: Computation of the Hartree-Fock Exchange in the Tensor-structured Format. Comp. Meth. in Applied Math., vol 10(2), 2010, 204-218.
|
|
B.N. Khoromskij, A. Litvinenko, and H.G. Matthies: Application of hierarchical matrices for computing the Karhunen-Loéve expansion. Computing 84: 49-67 (2009).
|
|
B.N. Khoromskij and V. Khoromskaia: Multigrid accelerated tensor approximation of function related multi-dimensional arrays. SIAM J. on Sci. Comp. 31(4), 3002-3026 (2009).
|
|
B.N. Khoromskij, V. Khoromskaia, S.R. Chinnamsettey, and H.-J. Flad. Tensor decomposition in electronic structure calculations on 3D Cartesian grids, J. of Comp. Phys. 228 (2009) 5749-5762.
|
|
M. Espig, W. Hackbusch, Th. Rohwedder, and R. Schneider: Variational Calculus with Sums of Elementary Tensors of Fixed Rank. Preprint 52/2009, MPI MiS, Leipzig, 2009, submitted.
|
|
S. W. Hackbusch, and S. Kühn, A new scheme for the tensor representation. J. Fourier Anal Appl (2009) 15: 706-722.
|
|
H.-J. Flad, W. Hackbusch, B.N. Khoromskij, and R. Schneider: Concept of Data-Sparse Tensor-Product Approximation in Many-Particle Modeling. In: "Matrix Methods: Theory, Algorithms, Applications", V. Olshevsky, E. Tyrtyshnikov eds.,World Scientific Publishing, Singapoure, 2010, pp. 313-347.
|
|
M. Espig, L. Grasedyck, and W. Hackbusch: Black Box Low Tensor Rank Approximation using Fibre-Crosses. Preprint 60/2008, MPI MiS, Leipzig, 2008, (Constr. Appr. 2009, accepted).
|
|
W. Hackbusch: Efficient convolution with the Newton potential in d dimensions. Numer. Math. 110 (3), 2008, 449-489.
|
|
W.Hackbusch, B.N. Khoromskij, S. Sauter and E. Tyrtyshnikov: Use of tensor formats in elliptic eigenvalue problems. Preprint 78/2008, MPI MiS Leipzig, 2008 (SIAM J. Num. Anal., submitted).
|
|
B.N. Khoromskij: On Tensor Approximation of Green Iterations for Kohn-Sham Equations. Computing and Visualization in Sci., 11: 259-271 (2008). Preprint 4, MPI MIS Leipzig,
|
|
B.N. Khoromskij: Fast and Accurate Tensor Approximation of Multivariate Convolution with Linear Scaling in Dimension. J. of Comp. Appl. Math., 234 (2010) 3122-3139.
|
|
C. Bertoglio, and B.N. Khoromskij: Low rank tensor-product approximation of projected Green kernels via sinc-quadratures. Preprint 79/2008, MPI MiS 2008 (submitted). (Computing, submitted).
|
|
H.-J. Flad, B. Khoromskij, D. Savostianov, and E. Tyrtyshnikov: Verification of the cross 3d algorithm on quantum chemistry data. Rus. J. Numer. Anal. and Math. Modelling, vol. 23, no. 4 (2008), pp. 210-220.
|
|
W. Hackbusch and B.N. Khoromskij. Tensor-product approximation to multi-dimensional integral operators and Green's functions. Preprint 38, MPI MIS, Leipzig 2006. SIAM J. Matr. Anal. Appl., 30, no. 3 (2008), 1233-1253.
|
|
W. Hackbusch, B.N. Khoromskij and E. Tyrtyshnikov. Approximate iteration for structured matrices. Numer. Math., 109 (2008), 365-383. http://dx.doi.org/10.1007/s00211-008-0143-0.
|
|
W. Hackbusch and B.N. Khoromskij. Tensor-product Approximation to Operators and Functions in High Dimension. Journal of Complexity 23 (2007), 697-714.
|
|
S.R. Chinnamsettey, M. Espig, B.N. Khoromskij, W. Hackbusch, and H.J. Flad. Tensor product approximation with optimal rank in quantum chemistry. The Journal of Chemical Physics 127, 084110 (2007).
|
|
B.N. Khoromskij and V. Khoromskaia. Low Rank Tucker-Type Tensor Approximation to Classical Potentials. Central European J. of Math. 5 (3) 2007, 1-28.
|
|
B.N. Khoromskij. Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation. Math. Comp. 76 (2007), 1292-1315.
|
|
B.N. Khoromskij: Structured Rank-(r1,...,rd) Decomposition of Function-related Operators in Rd. Comp. Meth. in Appl. Math. 6 (2006), No. 2, 194-220.
|
|
W. Hackbusch and B.N. Khoromskij: Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part II. HKT representations of certain operators. Computing 76 (2006), 203-225.
|
|
W. Hackbusch and B.N. Khoromskij: Low-rank Kronecker product approximation to multi-dimensional nonlocal operators. Part I. Separable approximation of multi-variate functions; Computing 76 (2006), 177-202.
|
|
I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij. Data-Sparse Approximation to a Class of Operator-Valued Functions. Math. Comp. 74 (2005), 681-708.
|
|
W. Hackbusch, B.N. Khoromskij and E. Tyrtyshnikov. Hierarchical Kronecker Tensor-Product Approximations. J. Numer. Math. Vol. 13, No. 2 (2005), 119-156.
|
|
I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij. Hierarchical Tensor-Product Approximation to the Inverse and Related Operators in High-Dimensional Elliptic Problems. Computing 74 (2005), 131-157.
|
|
B.N. Khoromskij. An Introduction to Structured Tensor-Product Approximation of Discrete Nonlocal Operators. MPI MiS, Lecture notes No. 27, Leipzig 2005, 1-279.
|
|
I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij. Data-Sparse Approximation to Operator-Valued Functions of Elliptic Operator. Math. Comp. 73 (2003), 1297-1324.
|
|
|
|
B.N. Khoromskij, and I.V. Oseledets: Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs. Preprint MPI MIs, Leipzig 2010 (submitted).
|
|
I. Oseledets, E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra Appl., 432 (2010), pp. 70-88.\\ Preprint 2009-05, INM RAS, 2009 (http://pub.inm.ras.ru).
|
|
I. Oseledets, E. Tyrtyshnikov, Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput., vol 31, no. 5 (2009), pp. 3744-3759.
|
|
S.V. Dolgov, B.N. Khoromskij, and E.E. Tyrtyshnikov, Tensor-Structured Solution of Elliptic Problems with Piecewise Smooth Coefficients. Leipzig, 2009 (in preparation).
|
|
B.N. Khoromskij, and I. V. Oseledets: Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions. Preprint 79/2009 MPI MiS, Leipzig, 2009 (submitted).
|
|
V.A.Kazeev, E.E.Tyrtyshnikov, The structure of Hessian and cost-effcient implementation of the Newton method in the problem of canonical approximation of tensors, Journal of Comp. Math. and Math. Physics, 2009 (submitted).
|
|
O.S.Lebedeva, A block method of the type of conjugate gradients for minimization of the Rayleigh quotient in two dimensions, Journal of Comp. Math. and Math. Physics, 2009 (accepted).
|
|
D. Savostyanov, Tensor methods for blind source separation, Rus. J. Num. Anal. and Math. Modelling, 2009 (submitted); Preprint 2009-09, INM RAS (http://pub.inm.ras.ru).
|
|
I.Oseledets, E. Tyrtyshnikov, Tensor tree decomposition does not a tree, Linear Algebra Appl., 2009 (submitted); Preprint 2009-08, INM RAS, 2009 (http://pub.inm.ras.ru).
|
|
I. Oseledets, Tensors inside matrices give logarithmic complexity, Preprint 2009-04, IMA RAS, 2009 (http://pub.inm.ras.ru); SIAM J. Matrix Anal. Appl. (accepted).
|
|
I. Oseledets, Compact matrix form of the d-dimesional tensor decomposition, Preprint 2009-01, INM RAS, 2009 (http://pub.inm.ras.ru); SIAM J. Sci. Comput. (accepted).
|
|
Oseledets I.V., Tyrtyshnikov E.E., Efficient and stable decompositions for multidimensional tensors, NOLTA Proceedings (2009),pp. 278-282.
|
|
S.A.Goreinov, D.V.Savostyanov, E.E.Tyrtyshnikov, Tensor and Toeplitz structures applied to direct and inverse 3D electromagnetic problems, Proc. PIERS (2009), pp. 1896-1900.
|
|
N.Zamarashkin, I.Oseledets, E.Tyrtyshnikov, The tensor structure of the inverse of a banded Toeplitz matrix, Doklady Mathematics, vol. 80, no. 2 (2009), pp. 669-670. (In Russian: Doklady Akademii Nauk, vol. 428, no. 2 (2009), pp. 161-162)
|
|
I.Oseledets, E.Tyrtyshnikov, Recursive decomposition of multidimensional tensors, Doklady Mathematics, vol. 80, no. 1 (2009), pp. 460-462. (In Russian: Doklady Akademii Nauk, vol. 427, no. 1 (2009), pp. 14-16)
|
|
D.Savostyanov, E.Tyrtyshnikov, Approximate multiplication of tensor matrices based on the individual filtering of factors, Comput. Math. and Math. Physics, vol.49, no.10 (2009), pp. 1662-1677. (In Russian: Zhurnal Vychisl. Matem. i Matem Fiziki, vol. 49, no. 10, 1741-1756)
|
|
Savostyanov D.V., Fast revealing of mode ranks of tensor in canonical format, Numer. Math. Theor. Meth. Appl. (2009), pp. 439-444.
|
|
E.Tyrtyshnikov, Preservation of linear constraints in approximation of tensors, Numer. Math. Theor. Meth. Appl. 2 (2009), pp. 421-426.
|
|
I.Oseledets, D. Savostyanov, E.Tyrtyshnikov, Linear algebra for tensor problems, Computing, 85 (2009), 169-188.
|
|
I.Oseledets, E.Tyrtyshnikov, N.Zamarashkin, Matrix inversion cases with size-independent tensor rank estimates, Linear Algebra Appl., 431 (2009), 558-570.
|
|
I.Oseledets, D.Savostyanov, E.Tyrtyshnikov, Fast simultaneous orthogonal reduction to triangular matrices, SIAM J. Matrix Anal. Appl., v. 31, no. 2, pp. 316-330 (2009).
|
|
W. Hackbusch, B.N. Khoromskij, S. Sauter, and E. Tyrtyshnikov, Use of tensor formats in elliptic eigenvalue problems. Preprint 78/2008, MPI MiS Leipzig, 2008 SIAM J. Num. Anal., (submitted).
|
|
S.Goreinov S., I.Oseledets, D.Savostyanov, E.Tyrtyshnikov, N.Zamarashkin, How to find a good submatrix, Research Report 08-10, ICM HKBU, November 2008.
|
|
S.A.Goreinov, On the cross approximation of a multi-index array, Doklady Math., vol. 420, no. 4 (2008), pp. 439-441.
|
|
E.Tyrtyshnikov, Tensor ranks for inversion of tensor-product binomials, J. Comput. and Appl. Math., 2008, accepted.
|
|
H.-J.Flad, B.N.Khoromskij, D.V.Savostyanov, E.E.Tyrtyshnikov, Verification of the cross 3d algorithm on quantum chemistry data, Rus. J. Numer. Anal and Math. Modelling, vol. 23, no. 4 (2008), pp. 210-220.
|
|
I.Oseledets, D.Savostyanov, E.Tyrtyshnikov, Tucker dimensionality reduction of three-dimensional arrays in linear time, SIMAX, vol. 30, no. 3, pp. 939-956 (2008).
|
|
W. Hackbusch, B.N. Khoromskij and E.E. Tyrtyshnikov, Approximate iterations for structured matrices, Numer. Math., vol.109, no. 3, pp. 365-383 (2008).
|
|
V.Olshevsky, I.Oseledets, E.Tyrtyshnikov, Superfast inversion of two-level Toeplitz matrices using Newton iteration and tensor-displacement structure, Operator Theory Advances and Applications, vol. 179, pp. 229-240 (2008).
|
|
V. Olshevsky, I. Oseledets, E. Tyrtyshnikov, Tensor properties of multilevel Toeplitz and related matrices, Linear Algebra Appl. 412 (2006), 1-21.
|
|
J.M.Ford and E.E.Tyrtyshnikov, Solving linear systems using wavelet compression combined with Kronecker product approximation, Numerical Algotrihms 40 (2005), 125-135.
|
|
W. Hackbusch, B.N. Khoromskij and E.E. Tyrtyshnikov, Hierarchical Kronecker tensor-product approximations, J. Numer. Math. 13 (2005), 119-156.
|
|
I.V.Oseledets and E.E.Tyrtyshnikov, Approximate inversion of matrices in the process of solving a hypersingular integral equation, Comp. Math. and Math. Phys.} 45, No. 2 (2005), 302-313 (translated from JVM i MF 45, No. 2 (2005), 315-326).
|
|
E.E.Tyrtyshnikov, Kronecker-product approximations for some function-related matrices, Linear Algebra Appl. 379 (2004), 423-437.
|
|
J.M.Ford, I.V.Oseledets, E.E.Tyrtyshnikov, Matrix approximations and solvers using tensor products and non-standard wavelet transforms related to irregular grids, Rus. J. Numer. Anal. and Math. Modelling, Vol. 19, No. 2 (2004), 185-204.
|
|
J.M. Ford, E.E. Tyrtyshnikov, Combining Kronecker product approximation with discrete wavelet transforms to solve dense, function-related systems, SIAM J. Sci. Comp., Vol. 25, No. 3 (2003), 961-981.
|
|
E.E. Tyrtyshnikov, Tensor approximations of matrices generated by asymptotically smooth functions, Sbornik: Mathematics 194, No. 5-6 (2003), 941-954 (translated from Mat. Sb. 194, No. 6 (2003), 146-160)
|
|
