Papers in Journals, from year 2000.
  1. B. N. Khoromskij and I. Oseledets.
    Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions.
    in progress, 2009.

  2. B. N. Khoromskij.
    O(d log n)-Quantics Approximation of n-d Tensors in High-Dimensional Operator Calculus.
    Preprint MPI MIS Leipzig, 2009.

  3. 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.

  4. B. N. Khoromskij.
    Tensor-structured Preconditioners and Approximate Inverse of Elliptic Operators in Rd .
    Preprint 82/2008, MPI MIS Leipzig, 2008.
    J. Constructive Approximation, DOI: 10.1007/s00365-009-9068-9, 2009.

  5. B. N. Khoromskij and Ch. Schwab.
    Tensor approximation of Multi-parametric Elliptic Problems in R^d.
    ETH Zuerich, 2008 (in progress).

  6. 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.
    SIAM J. Numer. Anal., submitted.

  7. 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.

  8. 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.

  9. 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 .

  10. B. N. Khoromskij and V. Khoromskaia.
    Multigrid Accelerated Tensor Approximation of Function Related Multi-dimensional Arrays.
    Preprint 40/2008, MPI MIS Leipzig,
    2008, SIAM Journal on Scientific Computing, vol. 31, No. 4, pp. 3002-3026.

  11. B. N. Khoromskij.
    Fast and Accurate Tensor Approximation of Multivariate Convolution with Linear Scaling in Dimension.
    Preprint 36/2008, MPI MIS Leipzig, 2008.
    J. Comp. Appl. Math., accepted.

  12. H.-J. Flad, W. Hackbusch, B. N. Khoromskij and R. Schneider.
    Concept of data-Sparse Tensor-Product Approximation in Many-Particle Modeling.
    Preprint 3/2008, MPI MIS Leipzig, 2008. World Sci.Publ. (to appear).

  13. B. N. Khoromskij.
    On Tensor Approximation of Green Iterations for Kohn-Sham equations.
    Computing and Visualisation in Science , (2008) 11:259-271, DOI:10.1007/s00791-008-0097-x,2008.
    Preprint 4/2008, MPI MIS Leipzig, 2008.

  14. 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.
    Journ. of Comp. Phys., accepted.

  15. 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).

  16. 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, pp.523-550.

  17. 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.

  18. W. Hackbusch and B. N. Khoromskij.
    Tensor-product Approximation to Multi-dimensional Integral Operators and Green's Functions.
    Journal of Complexity , 2007 , doi:10.1016/j.jco.2007.03.007.

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

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

  21. 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.

  22. 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.

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

  24. 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.

  25. 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.

  26. W. Hackbusch, B. N. Khoromskij and E. E. Tyrtyshnikov.
    Hierarchical Kronecker tensor-product approximations.
    Numer. Math. 13 (2005), pp. 119-156.

  27. 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.

  28. 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.

  29. 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.

  30. 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.

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

  32. B.N. Khoromskij and J.M. Melenk.
    Boundary concentrated finite element methods..
    SIAM Journal on Numerical Analysis 41 (2003), pp. 1-36.

  33. 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.

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

  35. 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.

  36. 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.

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

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

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

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

  41. 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.

  42. 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.

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

  44. 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.

  45. 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.

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

Papers in Journals, 1976-2000
  1. 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.

  2. 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.

  3. 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.

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

  5. 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.

  6. 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.

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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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).
  17. 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).

  18. 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.

  19. 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).

  20. 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).

  21. 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.

  22. 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).

  23. 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.

  24. 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).

  25. 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).

  26. 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).

  27. 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.

  28. 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.

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

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

  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, 1-92.

  5. B. N. Khoromskij.
    Data-Sparse Approximation of Integral Operators.
    MPI MIS, Lecture notes No. 17, Leipzig 2003, 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, 1-279.

Surveys
  1. 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).

  2. 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).

  3. 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).

Papers in Conference Proceedings
  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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).

  12. 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, to appear.

Selected Preprints
  1. 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).

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

  3. 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.

  4. 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.

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