Dissertations, Lecture Notes, Books
  1. B.N. Khoromskij.
    Iterative Newton-type methods for nonlinear problems of mathematical physics.
    PhD Dissertation, (Phys-Math.), JINR, Dubna, 1978, (in Russian).

  2. B.N. Khoromskij.
    Optimization of numerical algorithms for solving magnetostatics and theoretical physics problems.
    Dr. Sci. (Dr. habil.) Dissertation (Phys.-Math.) , JINR, 11-91-113, Dubna, 1991, (in Russian).

  3. B. N. Khoromskij and G. Wittum.
    Numerical Solution of Elliptic Differential Equations by Reduction to the Interface.
    Research monograph,
    LNCSE, No. 36, Springer-Verlag 2004.

  4. B. N. Khoromskij.
    Lectures on multilevel substructuring methods for elliptic differential equations.
    Preprint 98/4, ICA3, University of Stuttgart, 1998, pp.1-92.

  5. B. N. Khoromskij.
    Data-Sparse Approximation of Integral Operators.
    MPI MIS, Lecture notes No. 17, Leipzig 2003, pp.1-61.

  6. B. N. Khoromskij.
    An Introduction to Structured Tensor-Product Approximation of Discrete Nonlocal Operators.
    MPI MIS, Lecture notes No. 27, Leipzig 2005, pp.1-279.

  7. B. N. Khoromskij.
    Introduction to Tensor Numerical Methods in Scientific Computing.
    Lecture notes, Preprint 06-2011, University of Zuerich, Institute of Mathematics, 2011, pp.1-238.
    http://www.math.uzh.ch/fileadmin/math/preprints/06_11.pdf

  8. Boris N. Khoromskij
    Tensor Numerical Methods in Scientific Computing
    Research monograph, De Gruyter, Berlin, 2018.
    Radon Series on Computational and Applied Mathematics 19.

  9. Venera Khoromskaia, Boris N. Khoromskij
    Tensor Numerical Methods in Quantum Chemistry
    Research monograph, De Gruyter, Berlin, 2018.

  10. P. Benner, B. N. Khoromskij and V. Khoromskaia.
    Tensor-based surrogate approximation for the long-range electrostatics in polarizable many-body systems.
    Manuscript, 2023.

  11. P. Benner, B. N. Khoromskij, V. Khoromskaia and M. Stein.
    Benefits of tensor-based electrostatic energy calculations in the framework of protein-ligand docking problem.
    Manuscript, 2023.

  12. B. N. Khoromskij and V. Khoromskaia.
    Editorial: Tensor numerical methods and their application in scientific computing and data science. (Open access).
    Numer. Lin. Algebra Appl., doi/10.1002/nla.2493, 2023.

  13. B. N. Khoromskij and V. Khoromskaia.
    Fast solution of three-dimensional elliptic equations with randomly generated jumping
    coefficients by using tensor-structured preconditioners. (Open access).
    Numer. Lin. Algebra Appl., e2477, 2022.

  14. V. Khoromskaia and B. N. Khoromskij.
    Ubiquitous Nature of the Reduced Higher Order SVD in Tensor-Based Scientific Computing. (Open access).
    Frontiers in Applied Mathematics and Statistics,
    Special Issue: "High-Performance Tensor Computations in Scientific Computing and Data Science" (8), pp.144-164, 2022.

  15. B. Schmitt, B. N. Khoromskij, V. Khoromskaia, V. Schulz.
    Tensor method for optimal control problems constrained by fractional three-dimensional
    elliptic operator with variable coefficients. (Open access).
    Numer. Lin. Algebra Appl. , e2404, 2022.
    E-Preprint arXiv:2006.09314, 2020.

  16. C. Kweyu, V. Khoromskaia and B. N. Khoromskij, M. Stein, P. Benner.
    Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format.
    E-preprint arXiv:2109.14073, 2021.

  17. V. Khoromskaia and B. N. Khoromskij.
    Prospects of tensor-based numerical modeling of the collective electrostatic potential in many-particle systems. (Abstract).
    E-Preprint arXiv:2001.11393, 2020.
    Comput. Math. Math. Physics, 61 (5), 864-886, 2021.

  18. P. Benner, V. Khoromskaia, B. N. Khoromskij, C. Kweyu and M. Stein.
    Regularization of Poisson-Boltzmann type equations with singular source terms using the range-separated tensor format. (Abstract).
    SIAM J. Sci. Comput., 43 (1), A415-A445, 2021.

  19. V. Khoromskaia and B. N. Khoromskij.
    Tensor-based techniques for fast discretization and solution of 3D elliptic equations with random coefficients.
    E-Preprint arXiv:2007.06524, 2020.

  20. P. Benner, V. Khoromskaia, B. N. Khoromskij, C. Kweyu and M. Stein.
    Computing Electrostatic Potentials of Biomolecules using Regularization based on the Range-separated Tensor Format
    E-Preprint arXiv:1901.09864, 2019.

  21. V. Khoromskaia, B. N. Khoromskij and F. Otto.
    Numerical study in stochastic homogenization for elliptic partial differential equations: Convergence rate in the size of representative volume elements.
    E-preprint arXiv:1901.09864, 2019.
    Numer. Linear Algebra Appl., 27(3) 2020, e2296 (Open access).

  22. Boris N. Khoromskij.
    Range-separated Tensor Representation of the Discretized Multidimensional Dirac delta and Elliptic Operator Inverse.
    arxiv.org/abs/1812.02684, 2018.
    J. Comput. Physics, 401, 2020, pp.108998.

  23. G. Heidel, V. Khoromskaia, B. N. Khoromskij and V. Schulz.
    Tensor Approach to Optimal Control Problems with Fractional Multidimensional Elliptic Operator in Constraints. (Abstract).
    E-Preprint arXiv:1809.01971v1, 2018.
    J. Comput. Phys., 424, 109865, 2021.

  24. P. Benner, V. Khoromskaia and B. N. Khoromskij.
    Range-Separated Tensor Format for Many-particle Modeling.
    SIAM J. Sci. Comput., 40 (2), A1034-A1062, 2018.

  25. A. Litvinenko, D. Keyes, V. Khoromskaia, B. N. Khoromskij and H. G. Matthies
    Tucker tensor analysis of Matern functions in spatial statistics.
    Preprint, 2017, arXiv:1711.06874.
    Comput. Methods Appl. Math., 19(1), 2019, pp. 101-122.

  26. P. Benner, V. Khoromskaia, B. N. Khoromskij and C. Yang.
    Computing the Density of States for Optical Spectra of Molecules by Low-rank and QTT Tensor Approximation.
    E-preprint, arXiv:1801.03852, 2018, submitted.
    J. Comput. Physics, 382, 2019, pp. 221-239.

  27. S.V. Dolgov, V. Kazeev and B.N. Khoromskij.
    Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients.
    Mathematics and Computers in Simulation, 145, 136-155, 2018.

  28. V. Khoromskaia, B. N. Khoromskij and F. Otto.
    A Numerical Primer in 2D Stochastic Homogenization: CLT scaling in the Representative Volume Element.
    Preprint 47/2017 , Max-Planck Institute for Mathematics in the Sciences, Leipzig, 2017.

  29. B.N. Khoromskij and S. Repin.
    Rank structured approximation method for quasi--periodic elliptic problems.
    arXiv preprint arXiv:1701.00039, 2016.
    Comp. Meth. Appl. Math., 17 (3), 2017, pp.457-477.

  30. A. Mantzaflaris, B. J\"uttler, B.N. Khoromskij, and U. Langer.
    Low Rank Tensor Methods in Galerkin-based Isogeometric Analysis.
    Computer Methods in Applied Mechanics and Engineering, 316, 1062-1085, 2017.

  31. V. Khoromskaia and B. N. Khoromskij.
    Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach.
    Preprint 12/2017 , Max-Planck Institute for Mathematics in the Sciences, Leipzig, 2017.
    Comput. Methods Appl. Math., 17 (3), 431-455, 2017.
    (arXiv:1702.00339, 2017).

  32. P. Benner, V. Khoromskaia and B. N. Khoromskij.
    Range-separated Tensor Formats for Numerical Modeling of Many-particle Interaction Potentials.
    Preprint 39/2016, Max-Planck Institute for Mathematics in the Sciences, Leipzig, pp. 1-38, 2016.
    (arXiv:1606.09218, 2016).

  33. P. Benner, S. Dolgov, V. Khoromskaia and B. N. Khoromskij.
    Fast Iterative Solution of the Bethe-Salpeter Eigenvalue Problem Using Low-rank and QTT Tensor Approximation.
    Preprint 14/2016, Max-Planck Institute for Mathematics in the Sciences, Leipzig, 2016, (arXiv:1602.02646, 2016).
    J. Comp. Phys., 334, 2017 pp. 221-239.

  34. V. Khoromskaia and B. N. Khoromskij.
    Fast Tensor Method for Summation of Long-Range Potentials on 3D Lattices with Defects.
    Numer. Lin. Algebra Appl., 23, 2016, pp. 249-271.
    Preprint 65/2015 , MPI MIS Leipzig, 2015.

  35. P. Benner, V. Khoromskaia and B. N. Khoromskij.
    A Reduced Basis Approach for Calculation of the Bethe-Salpeter Excitation Energies using Low-Rank Tensor Factorizations.
    Molecular Physics, 114 (7-8) 2016.
    (arXiv:1505.02696), 2015.

  36. V. Khoromskaia and S. I. Repin.
    A fast iteration method for solving elliptic problems with quasiperiodic coefficients.
    Russian J. Numer. Analysis Math. Modelling, 30 (6), 329-344, 2015.

  37. V. Khoromskaia and B. N. Khoromskij.
    Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
    Physical Chemistry Chemical Physics, 17 (47), 31491-31509, 2015. (open access)
    (arXiv:1504.06289v1, 2015).

  38. A. Mantzaflaris, B. J\"uttler B.N. Khoromskij, and U. Langer.
    Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation.
    Curves and Surfaces, 321-340, 2014.
    Preprint RR-2014-22, Johann Radon Inst. for Comp. and Applied Mathematics, Linz, 2014.

  39. V. Khoromskaia and B. N. Khoromskij.
    Tucker tensor method for fast grid-based summation of long-range potentials on 3D lattices with defects.
    Preprint 88/2014 , MPI MIS Leipzig, 2014. arXiv:14.1994, 2014
    Numer. Lin. Algebra Appl., 23(2), 2016, pp. 249-271.

  40. B. N. Khoromskij and A. Veit.
    Efficient computation of highly oscillatory integrals by using QTT tensor approximation.
    Comp. Meth. Appl. Math. 16 (1), 145-159, 2016.
    E-preprint arXiv:1408.5224, 2014.

  41. Boris N. Khoromskij.
    Tensor Numerical Methods for High-dimensional PDEs: Basic Theory and Initial Applications.
    ESAIM: Proceedings and Surveys 48, 1-28, 2015.
    ArXiv:1408.4053, 2014.

  42. V. Khoromskaia and B. N. Khoromskij.
    Grid-based Lattice Summation of Electrostatic Potentials by Assembled Rank-structured Tensor Approximation.
    Comp. Phys. Communications, 185 (2014), pp. 3162-3174.
    ArXiv:1405.2270, 2014.

  43. V. Khoromskaia and B. N. Khoromskij.
    Tensor Approach to Linearized Hartree-Fock Equation for Lattice-type and Periodic Systems.
    Preprint 62/2014 , MPI MIS Leipzig, 2014.

  44. Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko, and Hermann G. Matthies.
    Computation of the Response Surface in the Tensor Train data format.
    SIAM J. Uncertainty Quantification, 3 (1), 1109-1135, 2015. Preprint 59/2014 , MPI MIS Leipzig, 2014.

  45. B. N. Khoromskij, S. Miao.
    Superfast Wavelet Transform Using QTT Approximation. I: Haar Wavelets.
    Preprint 103/2013, MPI MIS Leipzig, 2013.
    Comp. Meth. Appl. Math., Vol. 14(4), pp. 537 - 553, 2014.

  46. V. Khoromkaia and B. N. Khoromskij.
    Grid-based Ewald-type Lattice Summation of Electrostatic Potentials by Low-rank Tensor Approximation.
    Preprint 116/2013, MPI MIS Leipzig, 2013.

  47. V. Khoromskaia, B. N. Khoromskij.
    Moller-Plesset (MP2) Energy Correction using Tensor Factorization of the Grid-Based Two-Electron Integrals.
    Preprint 26/2013, MPI MIS Leipzig, 2013.
    Comp. Phys. Communications, 185 (2014) pp. 2-10.

  48. S. Dolgov, and B.N. Khoromskij.
    Simultaneous state-time approximation of the chemical master equation using tensor product formats.
    Numer. Lin. Algebra Appl. 22 (2), 197-219, 2015.
    arXiv:1311.3143, 2013; http://arxiv.org/abs/1311.3143.

  49. S. Dolgov, B.N. Khoromskij, D. Savostianov, and I. Oseledets.
    Computation of extreme eigenvalues in higher dimensions using block tensor train format.
    Preprint 59/2013, MPI MIS Leipzig, 2013, submitted.
    Comp. Phys. Communications, 185(4), 2014, pp. 1207-1216.

  50. S.V. Dolgov and B.N. Khoromskij.
    Tensor-product Approach to Global Time-space-parametric Discretization of Chemical Master Equation.
    Preprint 68/2012 MPI MiS Leipzig, 2012, submitted.

  51. S.V. Dolgov, V. Kazeev and B.N. Khoromskij.
    The Tensor-structured Solution of One-dimensional Elliptic Differential Equations with High-dimensional Parameters.
    Preprint 51/2012 MPI MiS Leipzig, 2012, submitted.

  52. V. Khoromskaia, B. N. Khoromskij and R. Schneider.
    Tensor-structured Factorized Calculation of Two-electron Integrals in a General Basis.
    Preprint 29/2012, MPI MIS Leipzig, 2012.
    SIAM J. Sci. Comp., Vol. 35, no. 2, A987-A1010, 2013.

  53. I. Oseledets, B.N. Khoromskij, and R. Schneider.
    Efficient time-stepping scheme for dynamics on TT manifolds.
    Preprint 24/2012 MPI MiS Leipzig, 2012.
    Computing and Visualisation in Science, 2014, to appear.

  54. S.V. Dolgov and B.N. Khoromskij.
    Two-level Tucker-TT-QTT format for optimized tensor calculus.
    Preprint 19/2012 MPI MiS Leipzig, 2012.
    SIAM J. Sci. Comp., 34 (2), 593-623, 2013.

  55. V. Khoromkaia, D. Andrae and B. N. Khoromskij.
    Fast and Accurate Tensor Calculation of the Fock Operator in a General Basis.
    Preprint 4/2012, MPI MIS Leipzig, 2012.
    Comp. Phys. Communications, 183 (2012) 2392-2404.

  56. S.V. Dolgov, B.N. Khoromskij, and I. Oseledets.
    Fast solution of multi-dimensional parabolic problems in the TT/QTT formats with initial application to the Fokker-Planck equation.
    Preprint 80/2011 MPI MiS Leipzig, 2011,
    SIAM J. Sci. Comp., 34(6), 2012, A3016-A3038.

  57. I. P. Gavrilyuk, and B. N. Khoromskij.
    Quantized-TT-Cayley transform to compute dynamics and spectrum of high-dimensional Hamiltonians.
    Preprint 43/2011 MPI MiS Leipzig, 2011.
    Comp. Meth. in Applied Math., v.11 (2011), No. 3, 273-290.

  58. B. N. Khoromskij, S. A. Sauter, and A. Veit.
    Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation.
    Preprint 42/2011 MPI MiS Leipzig, 2011.
    Comp. Meth. in Applied Math., v.11 (2011), No. 3, 342 - 362.

  59. S. V. Dolgov, B. N. Khoromskij, and D. Savostyanov.
    Superfast Fourier transform using QTT approximation.
    Preprint 18/2011 MPI MiS Leipzig, 2011,
    J. Fourier Anal. Appl., v. 18(5):915--953, 2012.

  60. V. Khoromkaia, B. N. Khoromskij and R. Schneider.
    QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations.
    Preprint 37/2011 MPI MiS Leipzig, 2011.
    Comp. Meth. in Applied Math., v.11 (2011), No. 3, 327-341.

  61. V. Kazeev, B. N. Khoromskij, and E. E. Tyrtyshnikov.
    Multilevel Toeplitz matrices generated by QTT tensor-structured vectors and convolution with logarithmic complexity.
    Preprint 36/2011 MPI MiS Leipzig, 2011,
    SIAM J. Sci. Comp., 35-3 (2013), pp. A1511-A1536.

  62. S. V. Dolgov, B. N. Khoromskij, I. Oseledets, and E. E. Tyrtyshnikov.
    Low-rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients.
    Preprint 12/2011 MPI MiS Leipzig, 2011.
    J. of Comput. Math. v. 30, No. 1, 2012, 14-23.

  63. V. Kazeev and B. N. Khoromskij.
    Explicit Low-rank QTT Representation of the Laplace Operator and its Inverse.
    Preprint 75/2010, MPI MiS, Leipzig 2010.
    SIAM J. Matr. Anal., 33(3), 2012, 742-758.

  64. B.N. Khoromskij, and I. Oseledets.
    DMRG + QTT approach to the computation of ground state for the molecular Schroedinger operator.
    Preprint 69/2010, MPI MiS, Leipzig 2010, submitted.

  65. B. N. Khoromskij.
    Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances.
    Preprint MPI MIS Leipzig 21/2010..
    Chemometr. Intell. Lab. Syst. 110 (2012), 1-19.
    http://dx.doi.org/10.1016/j.chemolab.2011.09.001

  66. B.N. Khoromskij, and I. Oseledets.
    Quantics-TT Collocation Approximation of Parameter-dependent and Stochastic Elliptic PDEs.
    Preprint 37/2010, MPI MIS Leipzig 2010.
    Comp. Meth. in Applied Math., 10(4):34-365, 2010.

  67. S. V. Dolgov, B. N. Khoromskij, I. Oseledets, and E. E. Tyrtyshnikov.
    A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients.
    Preprint 55/2010, MPI MiS, Leipzig 2010.
    Linear Algebra Appl. (2011), DOI: 10.1016/j.laa.2011.09.010

  68. B. N. Khoromskij and I. Oseledets.
    Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions.
    Preprint 79/2009, MPI MIS Leipzig, 2009.
    Russ. J. Numer. Anal. Math. Modelling, v. 26(3), pp. 303-322 (2011).

  69. B. N. Khoromskij.
    O(d log n)-Quantics Approximation of n-d Tensors in High-Dimensional Operator Calculus.
    Preprint 55/2009, MPI MIS Leipzig, 2009.
    J. Constructive Approximation, v. 34(2), 257-289 (2011).

  70. B. N. Khoromskij, V. Khoromskaia, and H.-J. Flad.
    Numerical Solution of the Hartree-Fock Equation in the Multilevel Tensor-Structured Format.
    Preprint 44/2009, MPI MIS Leipzig, 2009.
    SIAM J. Sci. Comp., v. 33(1), 2011, pp. 45-65.

  71. B. N. Khoromskij.
    Tensor-structured Preconditioners and Approximate Inverse of Elliptic Operators in Rd .
    Preprint 82/2008, MPI MIS Leipzig, 2008.
    J. Constructive Approximation, 30 (2009), 599-620.

  72. B. N. Khoromskij and Ch. Schwab.
    Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs.
    Preprint 9/2010, MPI MIS Leipzig, 2010.
    SIAM J. Sci. Comp. 33(1), 2011, 1-25.

  73. C. Bertoglio, and B. N. Khoromskij.
    Low Rank Tensor-product Approximation of Projected Green Kernels via Sinc-quadratures.
    Preprint 79/2008, MPI MIS Leipzig, 2008.
    Comp. Phys. Communications, v. 183(4), 904-912 (2012).

  74. H.-J. Flad, B. N. Khoromskij, D. Savostianov and E. Tyrtyshnikov.
    Verification of the Cross 3d Algorithm on Quantum Chemistry Data.
    Preprint 80/2008, MPI MIS Leipzig, 2008.
    Rus. J. Numer. Anal. and Math. Modelling, 4 (2008), 1-16 .

  75. B. N. Khoromskij and V. Khoromskaia.
    Multigrid Accelerated Tensor Approximation of Function Related Multi-dimensional Arrays.
    Preprint 40/2008, MPI MIS Leipzig, 2008,
    SIAM J. Sci. Comp., vol. 31, No. 4, (2009) pp. 3002-3026.

  76. B. N. Khoromskij.
    Fast and Accurate Tensor Approximation of a Multivariate Convolution with Linear Scaling in Dimension.
    Preprint 36/2008, MPI MIS Leipzig, 2008.
    J. Comp. Appl. Math., 234 (2010) 3122-3139.

  77. H.-J. Flad, W. Hackbusch, B. N. Khoromskij and R. Schneider.
    Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modeling.
    Preprint 3/2008, MPI MIS Leipzig, 2008.
    In: Matrix Methods: Theory, Algorithms and Applications, (dedicated to the Memory of Gene Golub)
    V. Olshevsky, E. Tyrtyshnikov eds., World Scientific, 2010, pp.313-347.

  78. B. N. Khoromskij.
    On Tensor Approximation of Green Iterations for Kohn-Sham equations.
    Preprint 4/2008, MPI MIS Leipzig, 2008.
    Computing and Visualisation in Science , (2008) 11:259-271.

  79. B. N. Khoromskij, V. Khoromskaia, S.R. Chinnamsetty and H.-J. Flad.
    Tensor Decomposition in Electronic Structure Calculations on 3D Cartesian Grids.
    Preprint 65/2007, MPI MIS Leipzig, 2007.
    J. Comp. Phys., 228, (2009) 5749-5762.

  80. W. Hackbusch, B. N. Khoromskij, S. Sauter and E. Tyrtyshnikov.
    Use of Tensor Formats in Elliptic Spectral Problems.
    Preprint 78/2008, MPI MIS Leipzig, 2008,
    Numer. Lin. Alg. Appl., v.19(1), 2012, 133-151.

  81. S.R. Chinnamsetty, M. Espig, B.N. Khoromskij, W. Hackbusch and H.-J. Flad.
    Tensor Product Approximation with Optimal Rank in Quantum Chemistry.
    Preprint 105, MPI MIS Leipzig, 2007.
    J. Chem. Phys., 127, 084110 (2007).

  82. B. N. Khoromskij and V. Khoromskaia.
    Low Rank Tucker-Type Tensor Approximation to Classical Potentials.
    Preprint 105/2006, MPI MIS Leipzig, 2006.
    Central European Journal of Mathematics v.5, N.3, 2007, 523-550.

  83. M.V. Fedorov, H.-J. Flad, G.N. Chuev, L. Grasedyck and B.N. Khoromskij.
    A Structured Low-rank Wavelet Solver for the Ornstein-Zernike Integral equation.
    Computing 80(1), 2007, 47-73.

  84. W. Hackbusch and B. N. Khoromskij.
    Tensor-product Approximation to Multi-dimensional Integral Operators and Green's Functions.
    Journal of Complexity , (23) 2007, 697-714.

  85. B. N. Khoromskij.
    Structured Data-sparse Approximation to High Order Tensors arising from the Deterministic Boltzmann equation.
    Math. Comp. 76 (2007), pp. 1292-1315.

  86. 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, 1233-1253, 2008.

  87. 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), pp. 177-202.

  88. B. N. Khoromskij.
    Structured Rank- (r1,...,rd) Decomposition of Function-related Tensors in Rd .
    Preprint 6/2006, MPI MIS Leipzig, 2006.
    Comp. Meth. in Appl. Math. , v.6, No.2, (2006), 194-220.

  89. W. Hackbusch and B. N. Khoromskij.
    Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators.
    Part II. HKT Representation of Certain Operators.
    Computing 76 (2006), pp. 203-225.

  90. W. Hackbusch, B. N. Khoromskij and E. E. Tyrtyshnikov.
    Approximate Iteration for Structured Matrices.
    Preprint 112, MPI MIS, Leipzig, 2005.
    Numer. Math. , 109, 365-383, 2008.

  91. 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.

  92. I. P. Gavrilyuk, W. Hackbusch and B. N. Khoromskij.
    Data-sparse approximation of a class of operator-valued functions.
    Math. Comp. 74 (2005), pp. 681-708.

  93. I. P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij.
    Data-sparse approximation to the operator-valued functions of elliptic operators.
    Math. Comp. 73 (2004), pp. 1297-1324.

  94. W. Hackbusch, B. N. Khoromskij and E. E. Tyrtyshnikov.
    Hierarchical Kronecker tensor-product approximations.
    Numer. Math. 13 (2005), pp. 119-156.
    Preprint 35/2003, MPI MIS Leipzig, 2003.


  95. W. Hackbusch, B. N. Khoromskij and S. A. Sauter.
    Adaptive Galerkin boundary element methods with panel clustering.
    Numer. Math. 105 (2007), pp. 603-631.

  96. B. N. Khoromskij, A. Litvinenko and H. G. Matthies.
    Application of hierarchical matrices for computing the Karhunen-Lo'eve expansion.
    Preprint 81/2008, MPI MIS Leipzig, 2008.
    Computing, 84:49-67, 2009.

  97. W. Hackbusch, B. N. Khoromskij and R. Kriemann.
    Direct Schur complement method by domain decomposition based on H-matrix approximation.
    Computing and Visualization in the Sciences (2005), pp. 179-188.

  98. W. Hackbusch, B.N. Khoromskij and R. Kriemann.
    Hierarchical matrices based on a weak admissibility criterion.
    Computing 73 (2004), pp. 207-243.

  99. L. Grasedyck, W. Hackbusch and B.N. Khoromskij.
    Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices.
    Computing , 70 (2003), 121-165.

  100. B.N. Khoromskij.
    Hierarchical Matrix Approximation to Green's Function via Boundary Concentrated FEM.
    Numer. Math. , v.11, No.3, (2003), 195-223.

  101. B.N. Khoromskij.
    Data-sparse Elliptic Operator Inverse Based on Explicit Approximation to the Green's Function.
    J. of Numer. Math. (2003) v.11 No. 2, 135-162.

  102. B.N. Khoromskij.
    Hierarchical Matrix Approximation to Green's Function via Boundary Concentrated FEM.
    J. of Numer. Math. , v.11, No.3, (2003), 195-223.

  103. B.N. Khoromskij and J.M. Melenk.
    Boundary Concentrated Finite Element Methods.
    SIAM J. Numer. Anal. , 41 (2003), pp.1-36.

  104. I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij.
    H-Matrix Approximation for the Operator Exponential with Applications.
    Numer. Math. (2002) 92: 83-111.

  105. W. Hackbusch and B.N. Khoromskij.
    Blended Kernel Approximation in the H-Matrix Techniques.
    Numer. Linear Algebra Appl. (2002) 9: 281-304.

  106. B.N. Khoromskij and J.M. Melenk.
    An Efficient Direct Solver for the Boundary Concentrated FEM in 2D.
    Computing 69: 91-117, 2002.

  107. W. Hackbusch and B.N. Khoromskij.
    Towards H-Matrix Approximation of the Linear Complexity.
    Operator Theory: Advances and Applications, Vol. 121, Birkhaeuser Verlag, 2001, 194-220.

  108. I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij.
    H-Matrix Approximation for Elliptic Solution Operator in Cylinder Domains.
    East-West J. of Numer. Math. , v. 9, 1, 2001, 25-58.

  109. W. Hackbusch and B. N. Khoromskij.
    A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems.
    Computing 64, 2000, 1, 21-47.

  110. W. Hackbusch and B.N. Khoromskij.
    H-Matrix Approximation on Graded Meshes.
    The Mathematics of Finite Elements and Applications X, MAFELAP 1999, J.R. Whiteman (ed), Elsevier, Amsterdam, Chapter 19, 307-316, 2000.

  111. W. Hackbusch, B.N. Khoromskij and S. Sauter..
    On H2-Matrices.
    In: Lectures on Applied Mathematics (H.-J. Bungartz, R. Hoppe, C. Zenger, eds.), Springer-Verlag, Berlin, 2000, 9-30.

  112. W. Hackbusch and B.N. Khoromskij.
    A Sparse H-Matrix Arithmetic: General Complexity Estimates.
    J. of Comp. and Appl. Math., 125 (2000) 479-501.

  113. B. N. Khoromskij and G. Wittum.
    Robust Schur complement method for strongly anisotropic elliptic equations.
    J. Numer. Linear Algebra with Appl., 6 (1999), 1-33.

  114. G.C. Hsiao, B.N. Khoromskij and W.L. Wendland.
    Preconditioning for Boundary Element Methods in Domain Decomposition.
    Ing. Analysis with Boundary Elements, 25 (2001) 323-338.

  115. B. N. Khoromskij and G. Wittum.
    Robust Schur complement method for strongly anisotropic elliptic equations.
    J. Numer. Linear Algebra with Appl., 6 (1999), 1-33.

  116. B. N. Khoromskij and G. Wittum.
    An asymptotically optimal Schur complement reduction for the Stokes equation.
    Numer. Math. 81 (1999) 3, 345-375.

  117. B.N. Khoromskij, G. E. Mazurkevich and G. Wittum.
    Frequency filtering for elliptic interface problems with Lagrange multipliers.
    SIAM J. Sci. Comp., v. 21, 2, 1999, 421-440.

  118. B. N. Khoromskij.
    On a sparse finite element approximation to the boundary Poincaré-Steklov operators of planar elasticity.
    In: "Analysis, Numerics and Applications of Differential and Integral Equations", Pitman Research Notes in Mathematics, A. Jefferey, R. G. Douglas and H. Brezis eds., 1997, 122-126.

  119. B.N. Khoromskij and G. Schmidt.
    A fast interface solver for the biharmonic Dirichlet problem on polygonal domains.
    Numer. Math. , 1998, 78: 577-596.

  120. G. Schmidt and B.N. Khoromskij.
    Boundary integral equations for the biharmonic Dirichlet problem in non-smooth domains.
    J. of Integral Equations and Applications , v. 11, 2, 1999, 217-253.

  121. B. N. Khoromskij and S. Proessdorf.
    Fast computations with harmonic Poincaré-Steklov operators on nested refined meshes.
    Advances in Comp. Math., 8 (1998), 111-135.

  122. B. N. Khoromskij and S. Proessdorf.
    Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation.
    Advances in Comp. Math. , 4 (1995), 331-355.

  123. B.N. Khoromskij and G. Schmidt.
    Asymptotically optimal interface solvers for the biharmonic Dirichlet problem on convex polygonal domains.
    ZAMM 76, Suppl. 1, 231-234, 1996.

  124. B.N. Khoromskij and G. Wittum.
    Robust iterative methods for elliptic problems with highly varying coefficients in thin substructures.
    Numer. Math. 73: 449-472, 1996.

  125. B.N. Khoromskij.
    On the fast computations with the inverse to harmonic potential operators via domain decomposition.
    J. Numer. Lin. Alg. with Applications , v. 3(2), 91-111, 1996.

  126. F.-K. Hebeker and B.N. Khoromskij.
    Geometry independent preconditioners for boundary interface operators in elliptic problems.
    East-West J. of Numer. Math., vol.2, No. 1, 1994, 47-63.

  127. B.N. Khoromskij and W.L. Wendland.
    Spectrally equivalent preconditioners for boundary equations in substructuring techniques.
    East-West J. of Numer. Math., vol.1, No.1, 1992, 1-26.

  128. B.N. Khoromskij, G.E.Mazurkevich, I.P.Yudin and E.P.Zhidkov.
    Numerical computations of space field distribution for the dipole magnet.
    Math. Modelling , v.2, No.5, 1990, pp. 8-17 (in Russian).
  129. B.N. Khoromskij, E.G. Nikonov and E.P. Zhidkov.
    Solution of eigenvalue problem for one class of hypersingular quasipotential integral equations.
    Math. Modelling , v. 1, No.11, 1989, 77-91 (in Russian).

  130. B.N. Khoromskij, G.E. Mazurkevich and E.P. Zhidkov.
    Domain decomposition method for magnetostatics nonlinear problems in combined formulation.
    Sov. J. Numer. Anal. Math. Modelling , North Holland, Antwerpen, vol.5, No.2, 1990, 120-165.

  131. B.N. Khoromskij, E.G. Nikonov and E.P. Zhidkov.
    Asymptotic error estimates of Galerkin method for one class of quasipotential equations.
    Zh.Vychisl. Mat i Mat. Fiz., 1990, 30, No.6, 1280-1292 (in Russian).

  132. B.N. Khoromskij and E.P. Zhidkov.
    Some cost-effective algorithms using Toeplitz-type matrices.
    In: Numerical Processes and Systems (6) . Nauka, Moscow, 1988, 134-144, (in Russian).

  133. B.N. Khoromskij and E.P. Zhidkov.
    Boundary integral equations on special surfaces and their applications.
    Sov. J. Numer. Anal. Math. Modelling , North Holland, Antwerpen, 1988, v.2, No. 6, 463-488.

  134. B.N. Khoromskij.
    Integral-difference method of solving the Dirichlet problem for the Laplace equation.
    Zh. Vychisl. Mat. i Mat. Fiz., 1984, 24, No.1, 53-64 (in Russian).

  135. E.A. Ayrjan, B.N. Khoromskij and E.P. Zhidkov.
    Fast relaxation method for solving the difference problem for the Poisson equation on a sequence of grids.
    Comp. Phys. Commun. 29(1983), 125-130.

  136. B.N. Khoromskij, M. Nguen and R. M. Yamaleev.
    Method for improving accuracy of discrete eigenvalue problem for integral-differential equations.
    Differentz. Uravnenia, 1980, 16, No.7, 1293-1302 (in Russian).

  137. B.N. Khoromskij, M. Nguen and E.P. Zhidkov.
    Method of improving accuracy of approximate solutions for nonlinear singular integral equations of Chew-Low type.
    Zh. Vych. Mat. i Mat. Fiz., 1981, 21, No.4, 962-969 (in Russian).

  138. B.N. Khoromskij, M. Nguen, I.P. Nedelkov and E.P. Zhidkov.
    On the investigation of one class of solutions for Chew-Low equations.
    Zh. Vychisl. Mat. i Mat. Fiz., 1979 19, No. 4, 998-1014 (in Russian).

  139. F.A. Gareev, S.A Goncharov, E.P. Zhidkov, I.V. Puzynin, B.N. Khoromskij and R. Yamaleev.
    Numerical solution of eigenvalue problems for nuclear theory integro-differential equations.
    U.S.S.R. Comput. Math. Math. Phys. 17 (1977), No.2, 116-128.

  140. B.N. Khoromskij and E.P. Zhidkov.
    On the local convergence of iterative methods for solving nonlinear operator equations.
    Dokl. Akad. Nauk SSSR, 231(1976), No. 5, 1052-1055; Soviet Math. Dokl. vol.17, No. 6, 1976.

  141. B.N. Khoromskij, E.K. Khristov, V. Lelek, J. Visner, E.P. Zhidkov and I. Ulegla.
    Iterative methods for solving the inverse scattering problem (Survey)}.
    In: Elementary Particles and Nuclear Physics, 9, v.3, Energoatomizdat, Moscow, 1978, pp.710-769 (in Russian).

  142. B.N. Khoromskij and E.P. Zhidkov.
    Numerical methods on a sequence of grids and their applications in magnetostatics and theoretical physics problems (Survey).
    In: Elementary Particles and Nuclear Physics, 19, v.3, Energoatomizdat, Moscow, 1988, pp.622-668 (in Russian).

  143. E.A. Ajryan, A. Fedorow, O. Juldashev, B.N. Khoromskij, I. Shelaev, E. Zhidkov.
    Numerical algorithms of magnet systems simulations for charged particles accelerators (Survey).
    In: Elementary Particles and Nuclear Physics, 21, v.1, Energoatomizdat, Moscow, 1990, pp.251-307 (in Russian).
  144. B.N. Khoromskij, G.E. Mazurkevich and E.P. Zhidkov.
    Combined Methods for solving quasi-linear elliptic problems in unbounded domain.
    In: Proc. of International Confertence on Numerical Methods and Applications, Sofia, Bulgaria, 1988, 197-206.

  145. M. Gregus, B.N. Khoromskij, G.E. Mazurkevich and E.P. Zhidkov.
    On approximation of nonlinear boundary integral equations for the combined method.
    In: Boundary Element Methods XI, 1989, Springer-Verlag, v. 2, (ed. Brebbia C.A.), 100-106.

  146. B.N. Khoromskij, G.E. Mazurkevich and E.P. Zhidkov.
    Box-type decomposition algorithms for solving 3-D elliptic problems.
    In: Proc. of Fourth International Symposium on Domain Decomposition Methods, SIAM, Philadelphia (1991), 213-222.

  147. B.N. Khoromskij and G.E. Mazurkevich.
    Preconditioners for one class of elliptic problems in nonsimply-connected domains.
    In: Proc. of V-th Conference on Domain Decomposition Methods ; SIAM Publ., Philadelphia (1992), 56-61.

  148. B. N. Khoromskij and G. Wittum.
    An asymptotically optimal substructuring method for the Stokes equation.
    In: Domain Decomposition Methods in Sciences and Engineering, P.E. Bjorstad, M.S. Espedal and D.E. Keyes eds., Domain Decomposition Press, Bergen 1998, 31-39.

  149. B. N. Khoromskij and G. Wittum.
    Robust interface reduction for highly anisotropic elliptic equations.
    Proceedings of 5-th EMG Conference, W. Hackbusch and G. Wittum eds., Lecture Notes in Comp. Science and Eng., Springer Verlag, 1998, 140-156.

  150. B. N. Khoromskij and G. Wittum.
    Towards a stable multilevel method for elliptic equations with jumping diffusion and anisotropy coefficients.
    NNFM, vol. 70, W. Hackbusch and G. Wittum eds., Vieweg-Verlag, 1999, 88-103.

  151. B. N. Khoromskij and G. Wittum.
    Robust preconditioning for elliptic equations with anisotropy and in presence of thin geometries.
    In: Proc. of ENUMATH II Conference, H.G. Bock et al. eds.,
    World Scientific, Singapore, 1999, 140-150.

  152. B.N. Khoromskij.
    Robust preconditioning for FEM/BEM interface elliptic problems with rough parameters.
    In: Proc. of 15-th GAMM Seminar, Kiel, 1999. Numerical Methods for Composites (W. Hackbusch and S. Sauter eds.), Vieweg-Verlag, 2000.

  153. W. Hackbusch, B.N. Khoromskij and R. Kriemann.
    Direct Schur Complement Method by Hierarchical Matrix Techniques.
    in: DDM15 Conference proceedings (D. Keyes, O. Widlund, R. Kornhueber (eds.) 2004.

  154. I. P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij.
    Data-Sparse Approximation to a Hierarchy of Operator-valued Functions.
    In: Proc. of 18-th GAMM Seminar, Leipzig 2002, 31-52 (ISBN 3-00-009258-7, http://www.mis.mpg.de).

  155. B. N. Khoromskij and Litvinenko.
    Domain Decomposition based H-matrix Preconditioner for the Skin Problem in 2D and 3D.
    Preprint 95, MPI MIS Leipzig 2006;
    in: DDM17 Conference proceedings, Lect. Notes Comput. Sci. Eng., Springer Berlin 2008, 175-182.

    Selected Preprints
  156. B.N.Khoromskij.
    High accuracy extrapolation method for solution of BVPs with operators invariant with respect to the rotation of coordinate system.
    Preprint JINR, P5-80-736, Dubna, 1980, 15pp. (in Russian).

  157. B.N. Khoromskij.
    Quasi-linear elliptic equations in the incomplete nonlinear formulation and methods for their preconditioning.
    Preprint JINR, E5-89-598, Dubna, 1989.

  158. B.N.Khoromskij.
    A preconditioning technique for the solution of 3-D elliptic problems by substructuring with cross-lines.
    Preprint JINR, E11-90-181, Dubna, 1990, 39pp.

  159. B.N. Khoromskij, G.E. Mazurkevich and E.G. Nikonov.
    Cost-effective computations with boundary interface operators in elliptic problems.
    Preprint JINR, E11-163-93, Dubna, 1993.

  160. B. N. Khoromskij.
    Direct and mixed Schur complement methods for the Stokes equation.
    Preprint 98/5, ICA3, University of Stuttgart, 1998.

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