B.N. Khoromskij. Iterative Newton-type methods for nonlinear problems of mathematical physics.
PhD Dissertation, (Phys-Math.), JINR, Dubna, 1978, (in Russian).
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).
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.
B. N. Khoromskij. Lectures on multilevel substructuring methods for elliptic differential equations.
Preprint 98/4, ICA3, University of Stuttgart, 1998, pp.1-92.
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
P. Benner, B. N. Khoromskij and V. Khoromskaia.
Tensor-based surrogate approximation for
the long-range electrostatics in polarizable many-body systems.
Manuscript, 2023.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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).
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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
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).
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).
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.
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.
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.
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).
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 .
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
B. N. Khoromskij.
Structured Data-sparse Approximation to High Order Tensors arising from the
Deterministic Boltzmann equation. Math. Comp. 76 (2007), pp. 1292-1315.
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.
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.
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.
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.
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.
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.
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.
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.
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.
W. Hackbusch, B. N. Khoromskij and S. A. Sauter.
Adaptive Galerkin boundary element methods with panel clustering. Numer. Math. 105 (2007), pp. 603-631.
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.
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.
W. Hackbusch, B.N. Khoromskij and R. Kriemann.
Hierarchical matrices based on a weak admissibility criterion. Computing 73 (2004), pp. 207-243.
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.
B.N. Khoromskij.
Hierarchical Matrix Approximation to Green's Function
via Boundary Concentrated FEM. Numer. Math. ,
v.11, No.3, (2003), 195-223.
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.
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.
B.N. Khoromskij and J.M. Melenk.
Boundary Concentrated Finite Element Methods. SIAM J. Numer. Anal. , 41 (2003), pp.1-36.
I.P. Gavrilyuk, W. Hackbusch and B.N. Khoromskij.
H-Matrix Approximation for the Operator Exponential with
Applications. Numer. Math. (2002) 92: 83-111.
W. Hackbusch and B.N. Khoromskij.
Blended Kernel Approximation in the H-Matrix Techniques. Numer. Linear Algebra Appl. (2002) 9: 281-304.
B.N. Khoromskij and J.M. Melenk.
An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. Computing 69: 91-117, 2002.
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.
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.
W. Hackbusch and B. N. Khoromskij.
A Sparse H-Matrix Arithmetic. Part II: Application
to Multi-Dimensional Problems. Computing 64, 2000, 1, 21-47.
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.
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.
W. Hackbusch and B.N. Khoromskij.
A Sparse H-Matrix Arithmetic: General Complexity Estimates. J. of Comp. and Appl. Math., 125 (2000) 479-501.
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.
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.
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.
B. N. Khoromskij and G. Wittum.
An asymptotically optimal Schur complement
reduction for the Stokes equation. Numer. Math. 81 (1999) 3, 345-375.
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.
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.
B.N. Khoromskij and G. Schmidt.
A fast interface solver for the
biharmonic Dirichlet problem on polygonal domains. Numer. Math. , 1998, 78: 577-596.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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).
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.
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).
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).
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.
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).
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.
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).
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).
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).
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.
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.
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).
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).
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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).
B.N. Khoromskij.
Quasi-linear elliptic equations in the incomplete nonlinear formulation
and methods for their preconditioning.
Preprint JINR, E5-89-598, Dubna, 1989.
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.
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.
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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