Ivan Oseledets

Associate Professor at Skoltech

I have been working at Skoltech from August 2013. Prior to joining Skoltech I was working in the Institute of Numerical Mathematics of Russian Academy of Sciences (INM RAS, Институт вычислительной математики РАН). I still have a part-time position in INM RAS.

Research interests

My main research interest are numerical algorithms for large-scale matrix and tensor problems. This includes very different directions, but the beauty is that often they can be treated by similar numerical methods.

Main achievements

My main achievement is the introduction and development of different algorithms in the Tensor Train (TT) format. Such kind of representations have been known for many years in physics (Matrix Product States, Tensor Networks, Transfer Matrices), but these results were lying dead for the numerical mathematics. Now they are becoming an important tool in different applications in biology, chemistry and data mining.

All publications, sorted by year

  1. Andrzej Cichocki, Anh-Huy Phan, Qibin Zhao, Namgil Lee, Ivan Oseledets, Masashi Sugiyama, and Danilo Mandic. Tensor networks for dimensionality reduction and large-scale optimization: part 2 applications and future perspectives. Foundations and Trends in Machine Learning, 9(6):431–673, 2017. [ bib ]
  2. Grigory Drozdov, Igor Ostanin, and Ivan Oseledets. Time-and memory-efficient representation of complex mesoscale potentials. J. Comp. Phys., 343:110–114, 2017. [ bib ]
  3. Alexander Fonarev, Oleksii Hrinchuk, Gleb Gusev, Pavel Serdyukov, and Ivan Oseledets. Riemannian optimization for skip-Gram negative sampling. arXiv preprint 1704.08059, 2017. URL: http://arxiv.org/abs/1704.8059. [ bib ]
  4. Evgeny Frolov and Ivan Oseledets. Tensor methods and recommender systems. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 2017. [ bib ]
  5. Valentin Khrulkov and Ivan Oseledets. Art of singular vectors and universal adversarial perturbations. arXiv preprint 1709.03582, 2017. URL: http://arxiv.org/abs/1709.03582. [ bib ]
  6. Valentin Khrulkov, Maxim Rakhuba, and Ivan Oseledets. Vico-Greengard-Ferrando quadratures in the tensor solver for integral equations. arXiv preprint 1704.01669, 2017. URL: http://arxiv.org/abs/1704.01669. [ bib ]
  7. I. V. Oseledets, G. V. Ovchinnikov, and A. M. Katrutsa. Fast, memory efficient low-rank approximation of SimRank. Journal of Complex Networks, 5(1):111–126, 2017. URL: http://arxiv.org/abs/1410.0717, doi:10.1093/comnet/cnw008. [ bib ]
  8. Ivan Oseledets, Maxim Rakhuba, and André Uschmajew. Alternating least squares as moving subspace correction. arXiv preprint 1709.07286, 2017. URL: http://arxiv.org/abs/1709.07286. [ bib ]
  9. Igor Ostanin, Ivan Tsybulin, Mikhail Litsarev, Ivan Oseledets, and Denis Zorin. Scalable topology optimization with the kernel-independent fast multipole method. Engineering Analysis with Boundary Elements, 83:123–132, 2017. [ bib ]
  10. Igor Ostanin, Denis Zorin, and Ivan Oseledets. Fast topological-shape optimization with boundary elements in two dimensions. Russian J. Numer. Anal. Math. Modell., 32(2):127–133, 2017. [ bib ]
  11. Igor Ostanin, Denis Zorin, and Ivan Oseledets. Parallel optimization with boundary elements and kernel independent fast multipole method. International Journal of Computational Methods and Experimental Measurements, 5(2):154–162, 2017. [ bib ]
  12. G. Ovchinnikov, D. Zorin, and I. Oseledets. Robust regularization of topology optimization problems with a posteriori error estimators. arXiv preprint 1705.07316, 2017. URL: http://arxiv.org/abs/1705.07316. [ bib ]
  13. A. Pavlov, G. Ovchinnikov, D. Derbyshev, D. Tsetserukou, and I. Oseledets. AA-ICP: iterative closest point with Anderson acceleration. arXiv preprint 1709.05479, 2017. URL: http://arxiv.org/abs/1709.05479. [ bib ]
  14. Vladislav Pimanov and Ivan Oseledets. Regularization of topology optimization problem by the FEM a posteriori error estimator. arXiv preprint 1706.03516, 2017. URL: http://arxiv.org/abs/1706.03516. [ bib ]
  15. Maxim Rakhuba and Ivan Oseledets. Jacobi-Davidson method on low-rank matrix manifolds. arXiv preprint 1605.03795, 2017. URL: http://arxiv.org/abs/1703.0906. [ bib ]
  16. Daria Sushnikova and Ivan Oseledets. Simple non-extensive sparsification of the hierarchical matrices. arXiv preprint 1705.04601, 2017. URL: http://arxiv.org/abs/1705.04601. [ bib ]
  17. A. V. Chertkov, I. V Oseledets, and M. V. Rakhuba. Robust discretization in quantized tensor train format for elliptic problems in two dimensions. arXiv preprint 1612.01166, 2016. URL: http://arxiv.org/abs/1612.01166. [ bib ]
  18. A. Cichocki, N. Lee, I. V. Oseledets, A. H. Phan, Q. Zhao, and D. Mandic. Low-rank tensor networks for dimensionality reduction and large-scale optimization problems: perspectives and challenges part 1. arXiv preprint 1609.00893, 2016. accepted at Trends and Foundations in Machine Learning. URL: http://arxiv.org/abs/1609.00893. [ bib ]
  19. Andrzej Cichocki, Namgil Lee, Ivan Oseledets, Anh-Huy Phan, Qibin Zhao, Danilo P Mandic, and others. Tensor networks for dimensionality reduction and large-scale optimization: part 1 low-rank tensor decompositions. Foundations and Trends in Machine Learning, 9(4-5):249–429, 2016. [ bib ]
  20. Alexander Fonarev, Alexander Mikhalev, Pavel Serdyukov, Gleb Gusev, and Ivan Oseledets. Efficient rectangular maximal-volume algorithm for rating elicitation in collaborative filtering. arXiv preprint 1610.04850, 2016. accepted at ICDM 2016. URL: http://arxiv.org/abs/1610.04850. [ bib ]
  21. Evgeny Frolov and Ivan Oseledets. Fifty shades of ratings: how to benefit from a negative feedback in top-n recommendations tasks. In Proceedings of the 10th ACM Conference on Recommender Systems, RecSys '16, 91–98. 2016. URL: http://arxiv.org/abs/1607.04228, doi:10.1145/2959100.2959170. [ bib ]
  22. Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, and Frank Verstraete. Unifying time evolution and optimization with matrix product states. Phys. Rev. B, 94(16):165116, 2016. URL: http://arxiv.org/abs/1408.5056, doi:10.1103/PhysRevB.94.165116. [ bib ]
  23. Vladimir Kazeev, Ivan Oseledets, Maxim Rakhuba, and Christoph Schwab. QTT-finite-element approximation for multiscale problems I: model problems in one dimension. Adv. Comp. Math., 2016. URL: http://www.sam.math.ethz.ch/reports/2016/06, doi:10.1007/s10444-016-9491-y. [ bib ]
  24. Valentin Khrulkov and Ivan Oseledets. Desingularization of bounded-rank matrix sets. arXiv preprint 1612.03973, 2016. URL: http://arxiv.org/abs/1612.03973. [ bib ]
  25. Denis Kolesnikov and Ivan Oseledets. Convergence analysis of projected fixed-point iteration on a low-rank matrix manifold. arXiv preprint 1604.02111, 2016. URL: http://arxiv.org/abs/1604.02111. [ bib ]
  26. M. S. Litsarev and I. V. Oseledets. Low-rank approach to the computation of path integrals. J. Comp. Phys., 305:557–574, 2016. URL: http://arxiv.org/abs/1504.06149, doi:10.1016/j.jcp.2015.11.009. [ bib ]
  27. A. Yu. Mikhalev and I. V. Oseledets. Iterative representing set selection fo nested cross approximation. Numer. Linear Algebra Appl., 23(2):230–248, 2016. URL: http://arxiv.org/abs/1309.1773, doi:10.1002/nla.2021. [ bib ]
  28. D. V. Nazarenko, P. V. Kharyuk, I. V. Oseledets, I. A. Rodin, and O. A. Shpigun. Machine learning for LC-MS medicinal plants identification. Chemometrics and Intelligent Laboratory Systems, 156:174–180, 2016. URL: http://www.sciencedirect.com/science/article/pii/S0169743916301368, doi:10.1016/j.chemolab.2016.06.003. [ bib ]
  29. Alexander Novikov, Mikhail Trofimov, and Ivan Oseledets. Tensor Train polynomial models via Riemannian optimization. arXiv preprint 1605.03795, 2016. URL: http://arxiv.org/abs/1605.03795. [ bib ]
  30. Ivan V. Oseledets, Maxim V. Rakhuba, and Andrei V. Chertkov. Black-box solver for multiscale modelling using the QTT format. In Proc. ECCOMAS. Crete Island, Greece, 2016. URL: https://www.eccomas2016.org/proceedings/pdf/10906.pdf. [ bib ]
  31. Igor Ostanin, Ivan Tsybulin, Mikhail Litsarev, Ivan Oseledets, and Denis Zorin. What lies beneath the surface: topological-shape optimization with the kernel-independent fast multipole method. arXiv preprint 1612.04082, 2016. URL: http://arxiv.org/abs/1612.04082. [ bib ]
  32. M. V. Rakhuba and I. V. Oseledets. Grid-based electronic structure calculations: the tensor decomposition approach. J. Comp. Phys., 2016. URL: http://arxiv.org/abs/1508.07632, doi:10.1016/j.jcp.2016.02.023. [ bib ]
  33. Maxim Rakhuba and Ivan Oseledets. Calculating vibrational spectra of molecules using tensor train decomposition. J. Chem. Phys., 145:124101, 2016. doi:10.1063/1.4962420. [ bib ]
  34. Daria A. Sushnikova and Ivan V. Oseledets. "compress and eliminate" solver for symmetric positive definite sparse matrices. arXiv preprint 1603.09133, 2016. URL: http://arxiv.org/abs/1603.09133. [ bib ]
  35. Daria A. Sushnikova and Ivan V. Oseledets. Preconditioners for hierarchical matrices based on their extended sparse form. Russ. J. Numer. Anal. Math. Modelling, 31(1):29–40, 2016. URL: http://arxiv.org/abs/1412.1253, doi:10.1515/rnam-2016-0003. [ bib ]
  36. V. Baranov and I. Oseledets. Fitting high-dimensional potential energy surface using active subspace and tensor train (AS+TT) method. J. Chem. Phys., pages 17107, 2015. doi:10.1063/1.4935017. [ bib ]
  37. Sergey I. Kabanikhin, Nikita S. Novikov, Ivan V. Oseledets, and Maxim A. Shishlenin. Fast Toeplitz linear system inversion for solving two-dimensional acoustic inverse problem. Inverse Problems, 23(6):687–700, 2015. doi:10.1515/jiip-2015-0083. [ bib ]
  38. D. A. Kolesnikov and I. V. Oseledets. From low-rank approximation to arational Krylov subspace method for the Lyapunov equation. SIAM J. Matrix Anal. Appl., 36(4):1622–1637, 2015. URL: http://arxiv.org/abs/1410.3335, doi:10.1137/140992266. [ bib ]
  39. M. S. Litsarev and I. V. Oseledets. Fast low-rank approximations of multidimensional integrals in ion-atomic collisions modelling. Numer. Linear Algebra Appl., 22(6):1147–1160, 2015. URL: http://arxiv.org/abs/1403.4068, doi:10.1002/nla.2008. [ bib ]
  40. Christian Lubich, Ivan Oseledets, and Bart Vandereycken. Time integration of tensor trains. SIAM J. Numer. Anal., 53(2):917–941, 2015. URL: http://arxiv.org/abs/1407.2042, doi:10.1137/140976546. [ bib ]
  41. A. Yu. Mikhalev and I. V. Oseledets. Rectangular maximum-volume submatrices and their applications. arXiv preprint 1502.07838, 2015. URL: http://arxiv.org/abs/1502.07838. [ bib ]
  42. I. V. Oseledets, G. V. Ovchinnikov, and A. M. Katrutsa. Linear complexity SimRank using iterative diagonal estimation. arXiv preprint 1502.07167, 2015. URL: http://arxiv.org/abs/1502.07167. [ bib ]
  43. I. Ostanin, A. Mikhalev, D. Zorin, and I. Oseledets. Engineering optimization with the fast boundary element method. WIT Transactions on Modelling and Simulation, 61:7, 2015. doi:10.2495/BEM380141. [ bib ]
  44. Igor Ostanin, Denis Zorin, and Ivan Oseledets. Toward fast topological-shape optimization. arXiv preprint 1503.02383, 2015. URL: http://arxiv.org/abs/1503.02383. [ bib ]
  45. M. V. Rakhuba and I. V. Oseledets. Fast multidimensional convolution in low-rank tensor formats via cross approximation. SIAM J. Sci. Comput., 37(2):A565–A582, 2015. doi:10.1137/140958529. [ bib ]
  46. G.V. Ryzhakov, A.Yu. Mikhalev, D.A. Sushnikova, and I.V. Oseledets. Numerical solution of diffraction problems using large matrix compression. In Antennas and Propagation (EuCAP), 2015 9th European Conference on, 1–3. April 2015. URL: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=7228667&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D7228667. [ bib ]
  47. Ben Usman and Ivan Oseledets. Tensor SimRank for heterogeneous information networks. arXiv preprint 1502.06818, 2015. URL: http://arxiv.org/abs/1502.06818. [ bib ]
  48. Zhang Zheng, Xiu Yang, Ivan V. Oseledets, George Em Karniadakis, and Luca Daniel. Enabling high-dimensional hierarchical uncertainty quantification by ANOVA and Tensor-Train decomposition. IEEE Trans. Comput-aided Des. Integr. Circuits Syst., 34(1):63–76, 2015. URL: http://arxiv.org/abs/1407.3023, doi:10.1109/TCAD.2014.2369505. [ bib ]
  49. P. -A. Absil and I. V. Oseledets. Low-rank retractions: a survey and new results. Comput. Optim. Appl., 2014. URL: http://sites.uclouvain.be/absil/2013.04, doi:10.1007/s10589-014-9714-4. [ bib ]
  50. M. A. Botchev, I. V. Oseledets, and E. E. Tyrtyshnikov. Iterative across-time solution of linear differential equations: Krylov subspace versus waveform relaxation. Comput. Math. Appl., 67(2):2088–2098, 2014. doi:10.1016/j.camwa.2014.03.002. [ bib ]
  51. Anwesha Chaudhury, Ivan Oseledets, and Rohit Ramachandran. A computationally efficient technique for the solution of multi-dimensional PBMs of granulation. Comput. Chem. Eng., 61(11):234–244, 2014. doi:10.1016/j.compchemeng.2013.10.020. [ bib ]
  52. S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, and D. V. Savostyanov. Computation of extreme eigenvalues in higher dimensions using block tensor train format. Computer Phys. Comm., 185(4):1207–1216, 2014. doi:10.1016/j.cpc.2013.12.017. [ bib ]
  53. Vadim Lebedev, Yaroslav Ganin, Maxim Rakhuba, Ivan Oseledets, and Victor Lempitsky. Speeding up convolutional neural networks using fine-tuned CP-decomposition. arXiv preprint 1412.6553, 2014. URL: http://arxiv.org/abs/1412.6553. [ bib ]
  54. Mikhail S. Litsarev and Ivan V. Oseledets. The DEPOSIT computer code based on the low rank approximations. Computer Phys. Comm., 185(10):2801–2082, 2014. doi:10.1016/j.cpc.2014.06.012. [ bib ]
  55. Christian Lubich and Ivan V. Oseledets. A projector-splitting integrator for dynamical low-rank approximation. BIT, 54(1):171–188, 2014. doi:10.1007/s10543-013-0454-0. [ bib ]
  56. Ivan Oseledets. Solving high-dimensional problems via stable and efficient tensor factorization techniques. In Abstracts of Papers of the American Chemical Society, volume 246, 244–Phys. 2014. [ bib ]
  57. G. V. Ovchinnikov, D. A. Kolesnikov, and I. V. Oseledets. Algebraic reputation model RepRank and its application to spambot detection. arXiv preprint 1411.5995, 2014. URL: http://arxiv.org/abs/1411.5995. [ bib ]
  58. Vladimir A. Kazeev and Ivan V. Oseledets. The tensor structure of a class of adaptive algebraic wavelet transforms. Preprint 2013-28, ETH SAM, Zürich, 2013. URL: http://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-28.pdf. [ bib ]
  59. Vladimir Lyashev, Ivan Oseledets, and Delai Zheng. Tensor-based multiuser detection and intra-cell interference mitigation in LTE PUCCH. In Proc. TELFOR 2013, 385–388. 2013. doi:10.1109/TELFOR.2013.6716250. [ bib ]
  60. E.A. Muravleva and I.V. Oseledets. Fast low-rank solution of the Poisson equation with application to the Stokes problem. arXiv preprint 1306.2150, 2013. URL: http://arxiv.org/abs/1306.2150. [ bib ]
  61. I. V. Oseledets. Constructive representation of functions in low-rank tensor formats. Constr. Approx., 37(1):1–18, 2013. doi:10.1007/s00365-012-9175-x. [ bib ]
  62. S. V. Dolgov, Boris N. Khoromskij, and Ivan V. Oseledets. Fast solution of multi-dimensional parabolic problems in the tensor train/quantized tensor train–format with initial application to the Fokker-Planck equation. SIAM J. Sci. Comput., 34(6):A3016–A3038, 2012. doi:10.1137/120864210. [ bib ]
  63. S. V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets, and Eugene E. Tyrtyshnikov. Low-rank tensor structure of solutions to elliptic problems with jumping coefficients. J. Comput. Math., 30(1):14–23, 2012. URL: http://www.mis.mpg.de/de/publications/preprints/2011/prepr2011-12.html, doi:10.4208/jcm.1110-m11si08. [ bib ]
  64. Sergey Dolgov, Boris N. Khoromskij, Ivan V. Oseledets, and Eugene E. Tyrtyshnikov. A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients. Linear Algebra Appl., 436(9):2980–3007, 2012. doi:10.1016/j.laa.2011.09.010. [ bib ]
  65. S. A. Goreinov, I. V. Oseledets, and D. V. Savostyanov. Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case. SIAM J. Sci. Comput., 34(1):A1–A27, 2012. doi:10.1137/100792056. [ bib ]
  66. I. V. Oseledets and S. V. Dolgov. Solution of linear systems and matrix inversion in the TT-format. SIAM J. Sci. Comput., 34(5):A2718–A2739, 2012. doi:10.1137/110833142. [ bib ]
  67. I. V. Oseledets, B. N. Khoromskij, and R. Schneider. Efficient time-stepping scheme for dynamics on TT-manifolds. Preprint 24, MPI MIS, 2012. URL: http://www.mis.mpg.de/preprints/2012/preprint2012_24.pdf. [ bib ]
  68. I. V. Oseledets and A. Yu Mikhalev. Representation of quasiseparable matrices using excluded sums and equivalent charges. Linear Algebra Appl., 436(3):699–708, 2012. doi:10.1016/j.laa.2011.07.041. [ bib ]
  69. B. N. Khoromskij and I. V. Oseledets. QTT-approximation of elliptic solution operators in higher dimensions. Rus. J. Numer. Anal. Math. Model., 26(3):303–322, 2011. doi:10.1515/rjnamm.2011.017. [ bib ]
  70. I. V. Oseledets. Improved n-term Karatsuba-like formulas in GF(2). IEEE Trans. Computers, 60(8):1212–1216, 2011. doi:10.1109/TC.2010.233. [ bib ]
  71. I. V. Oseledets. Tensor train decomposition for low-parametric representation of high-dimensional arrays and functions: Review of recent results. In Proceedings of 7th International Workshop on Multidimensional Systems (nDS). IEEE, 2011. doi:10.1109/nDS.2011.6076872. [ bib ]
  72. I. V. Oseledets. Tensor-train decomposition. SIAM J. Sci. Comput., 33(5):2295–2317, 2011. doi:10.1137/090752286. [ bib ]
  73. I. V. Oseledets. DMRG approach to fast linear algebra in the TT–format. Comput. Meth. Appl. Math., 11(3):382–393, 2011. doi:10.2478/cmam-2011-0021. [ bib ]
  74. I. V. Oseledets, S. Dolgov, V. Kazeev, D. Savostyanov, O. Lebedeva, P. Zhlobich, T. Mach, and L. Song. TT-Toolbox. 2011. https://github.com/oseledets/TT-Toolbox. URL: https://github.com/oseledets/TT-Toolbox. [ bib ]
  75. I. V. Oseledets and E. E. Tyrtyshnikov. Algebraic wavelet transform via quantics tensor train decomposition. SIAM J. Sci. Comput., 33(3):1315–1328, 2011. doi:10.1137/100811647. [ bib ]
  76. I. V. Oseledets, E. E. Tyrtyshnikov, and N. L. Zamarashkin. Tensor-train ranks of matrices and their inverses. Comput. Meth. Appl. Math, 11(3):394–403, 2011. [ bib ]
  77. D. V. Savostyanov and I. V. Oseledets. Fast adaptive interpolation of multi-dimensional arrays in tensor train format. In Proceedings of 7th International Workshop on Multidimensional Systems (nDS). IEEE, 2011. doi:10.1109/nDS.2011.6076873. [ bib ]
  78. S. Dolgov, B. Khoromskij, I. V. Oseledets, and E. E. Tyrtyshnikov. Tensor structured iterative solution of elliptic problems with jumping coefficients. Preprint 55, MPI MIS, Leipzig, 2010. URL: http://www.mis.mpg.de/preprints/2010/preprint2010_55.pdf. [ bib ]
  79. S. A. Goreinov, I. V. Oseledets, D. V. Savostyanov, E. E. Tyrtyshnikov, and N. L. Zamarashkin. How to find a good submatrix. In V. Olshevsky and E. Tyrtyshnikov, editors, Matrix Methods: Theory, Algorithms, Applications, pages 247–256. World Scientific, Hackensack, NY, 2010. [ bib ]
  80. B. N. Khoromskij and I. V. Oseledets. DMRG+QTT approach to computation of the ground state for the molecular Schrödinger operator. Preprint 69, MPI MIS, Leipzig, 2010. URL: http://www.mis.mpg.de/preprints/2010/preprint2010_69.pdf. [ bib ]
  81. B. N. Khoromskij and I. V. Oseledets. Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs. Comput. Methods Appl. Math., 10(4):376–394, 2010. doi:10.2478/cmam-2010-0023. [ bib ]
  82. I. V. Oseledets. Approximation of $2^d \times 2^d$ matrices using tensor decomposition. SIAM J. Matrix Anal. Appl., 31(4):2130–2145, 2010. doi:10.1137/090757861. [ bib ]
  83. I. V. Oseledets and E. A. Muravleva. Fast orthogonalization to the kernel of discrete gradient operator with application to the Stokes problem. Linear Algebra Appl., 432(6):1492–1500, 2010. doi:10.1016/j.laa.2009.11.010. [ bib ]
  84. I. V. Oseledets, D. V. Savostyanov, and E. E. Tyrtyshnikov. Cross approximation in tensor electron density computations. Numer. Linear Algebra Appl., 17(6):935–952, 2010. doi:10.1002/nla.682. [ bib ]
  85. I. V. Oseledets and E. E. Tyrtyshnikov. TT-cross approximation for multidimensional arrays. Linear Algebra Appl., 432(1):70–88, 2010. doi:10.1016/j.laa.2009.07.024. [ bib ]
  86. I. V. Oseledets. A new tensor decomposition. Doklady Math., 80(1):495–496, 2009. doi:10.1134/S1064562409040115. [ bib ]
  87. I. V. Oseledets. Approximation of matrices with logarithmic number of parameters. Doklady Math., 428(1):23–24, 2009. doi:10.1134/S1064562409050056. [ bib ]
  88. I. V. Oseledets, D. V. Savostyanov, and E. E. Tyrtyshnikov. Fast simultaneous orthogonal reduction to triangular matrices. SIAM J. Matrix Anal. Appl., 31(2):316–330, 2009. doi:10.1137/060650738. [ bib ]
  89. I. V. Oseledets, D. V. Savostyanov, and E. E. Tyrtyshnikov. Linear algebra for tensor problems. Computing, 85(3):169–188, 2009. doi:10.1007/s00607-009-0047-6. [ bib ]
  90. I. V. Oseledets, S. L. Stavtsev, and E. E. Tyrtyshnikov. Integration of oscillating functions in a quasi-threedimensional electrodynamic problem. Comput. Math. Math. Phys, 49(2):301–312, 2009. doi:10.1134/S0965542509020092. [ bib ]
  91. 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(5):3744–3759, 2009. doi:10.1137/090748330. [ bib ]
  92. I. V. Oseledets and E. E. Tyrtyshnikov. Recursive decomposition of multidimensional tensors. Doklady Math., 427(1):14–16, 2009. doi:10.1134/S1064562409040036. [ bib ]
  93. I. V. Oseledets and E. E. Tyrtyshnikov. Tensor tree decomposition does not need a tree. Preprint (Submitted to Linear Algebra Appl) 2009-04, INM RAS, Moscow, 2009. URL: http://pub.inm.ras.ru/pub/inmras2009-08.pdf. [ bib ]
  94. I. V. Oseledets, E. E. Tyrtyshnikov, and N. L. Zamarashkin. Matrix inversion cases with size-independent rank estimates. Linear Algebra Appl., 431(5-7):558–570, 2009. doi:10.1016/j.laa.2009.03.001. [ bib ]
  95. I. V. Oseledets, E. E. Tyrtyshnikov, and N. L. Zamarashkin. Tensor structure of the inverse of a banded Toeplitz matrix. Doklady Math., 80(2):669–670, 2009. doi:10.1134/S106456240905010X. [ bib ]
  96. V. Olshevsky, I. V. Oseledets, and E. E. Tyrtyshnikov. Superfast inversion of two-level Toeplitz matrices using Newton iteration and tensor-displacement structure. Operator Theory: Advances and Applications, 179:229–240, 2008. doi:10.1007/978-3-7643-8539-2_14. [ bib ]
  97. I. V. Oseledets. Optimal Karatsuba-like formulae for certain bilinear forms in GF(2). Linear Algebra Appl., 429(8):2052–2066, 2008. doi:10.1016/j.laa.2008.06.004. [ bib ]
  98. I. V. Oseledets. The integral operator with logarithmic kernel has only one positive eigenvalue. Linear Algebra Appl., 428(7):1560–1564, 2008. [ bib ]
  99. I. V. Oseledets, D. V. Savostianov, and E. E. Tyrtyshnikov. Tucker dimensionality reduction of three-dimensional arrays in linear time. SIAM J. Matrix Anal. Appl., 30(3):939–956, 2008. doi:10.1137/060655894. [ bib ]
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  101. V. Olshevsky, I. V. Oseledets, and E. E. Tyrtyshnikov. Tensor properties of multilevel Toeplitz and related matrices. Linear Algebra Appl., 412(1):1–21, 2006. doi:10.1016/j.laa.2005.03.040. [ bib ]
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  105. I. V. Oseledets. Use of divided differences and B-splines for constructing fast discrete transforms of wavelet type on nonuniform grids. Math. Notes, 77(5-6):686–694, 2005. [ bib ]
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26/05/2016 A TT-eigenvalue solver that finally works Papers
12/05/2016 Exponential machines and tensor trains Papers
06/04/2016 Convergence analysis of a projected fixed-point iteration Papers
30/03/2016 Compress-and-eliminate solver for sparse matrices Papers
01/12/2015 New paper in SIMAX Papers


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