Boris N. Khoromskij

Publication Activity (10 Years)

Years Active: 1995-2023
Publications (10 Years): 27

Top Topics

Scientific Computing

Differential Equations

Top Venues

Comput. Methods Appl. Math.

Numer. Linear Algebra Appl.

J. Comput. Phys.

Publications

Boris N. Khoromskij, Venera Khoromskaia
Editorial: Tensor numerical methods and their application in scientific computing and data science. Numer. Linear Algebra Appl. 30 (3) (2023)
Boris N. Khoromskij, Venera Khoromskaia
Fast solution of three-dimensional elliptic equations with randomly generated jumping coefficients by using tensor-structured preconditioners. Numer. Linear Algebra Appl. 30 (3) (2023)
Venera Khoromskaia, Boris N. Khoromskij
Ubiquitous Nature of the Reduced Higher Order SVD in Tensor-Based Scientific Computing. Frontiers Appl. Math. Stat. 8 (2022)
Britta Schmitt, Boris N. Khoromskij, Venera Khoromskaia, Volker Schulz
Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients. Numer. Linear Algebra Appl. 29 (1) (2022)
Venera Khoromskaia, Boris N. Khoromskij
Reduced Higher Order SVD: ubiquitous rank-reduction method in tensor-based scientific computing. CoRR (2022)
Peter Benner, Venera Khoromskaia, Boris N. Khoromskij, Cleophas Kweyu, Matthias Stein
Regularization of Poisson-Boltzmann Type Equations with Singular Source Terms Using the Range-Separated Tensor Format. SIAM J. Sci. Comput. 43 (1) (2021)
Gennadij Heidel, Venera Khoromskaia, Boris N. Khoromskij, Volker Schulz
Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints. J. Comput. Phys. 424 (2021)
Boris N. Khoromskij, Britta Schmitt, Volker Schulz
Tensor numerical method for optimal control problems constrained by an elliptic operator with general rank-structured coefficients. CoRR (2021)
Cleophas Kweyu, Venera Khoromskaia, Boris N. Khoromskij, Matthias Stein, Peter Benner
Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format. CoRR (2021)
Venera Khoromskaia, Boris N. Khoromskij
Tensor-based techniques for fast discretization and solution of 3D elliptic equations with random coefficients. CoRR (2020)
Boris N. Khoromskij
Range-separated tensor decomposition of the discretized Dirac delta and elliptic operator inverse. J. Comput. Phys. 401 (2020)
Venera Khoromskaia, Boris N. Khoromskij
Prospects of tensor-based numerical modeling of the collective electrostatic potential in many-particle systems. CoRR (2020)
Britta Schmitt, Boris N. Khoromskij, Venera Khoromskaia, Volker Schulz
Tensor Method for Optimal Control Problems Constrained by Fractional 3D Elliptic Operator with Variable Coefficients. CoRR (2020)
Venera Khoromskaia, Boris N. Khoromskij, Felix Otto
Numerical study in stochastic homogenization for elliptic partial differential equations: Convergence rate in the size of representative volume elements. Numer. Linear Algebra Appl. 27 (3) (2020)
Peter Benner, Venera Khoromskaia, Boris N. Khoromskij, Chao Yang
Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation. J. Comput. Phys. 382 (2019)
Alexander Litvinenko, David E. Keyes, Venera Khoromskaia, Boris N. Khoromskij, Hermann G. Matthies
Tucker Tensor Analysis of Matérn Functions in Spatial Statistics. Comput. Methods Appl. Math. 19 (1) (2019)
Boris N. Khoromskij, Kishore Kumar Naraparaju, Jan Schneider
Quantized CP approximation and sparse tensor interpolation of function-generated data. Numer. Linear Algebra Appl. 26 (5) (2019)
Ivan P. Gavrilyuk, Boris N. Khoromskij
Tensor Numerical Methods: Actual Theory and Recent Applications. Comput. Methods Appl. Math. 19 (1) (2019)
Ivan P. Gavrilyuk, Boris N. Khoromskij
Quasi-Optimal Rank-Structured Approximation to Multidimensional Parabolic Problems by Cayley Transform and Chebyshev Interpolation. Comput. Methods Appl. Math. 19 (1) (2019)
Peter Benner, Venera Khoromskaia, Boris N. Khoromskij
Range-Separated Tensor Format for Many-Particle Modeling. SIAM J. Sci. Comput. 40 (2) (2018)
Sergey Dolgov, Vladimir A. Kazeev, Boris N. Khoromskij
Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients. Math. Comput. Simul. 145 (2018)
Boris N. Khoromskij, Sergey I. Repin
Rank Structured Approximation Method for Quasi-Periodic Elliptic Problems. Comput. Methods Appl. Math. 17 (3) (2017)
Peter Benner, Sergey Dolgov, Venera Khoromskaia, Boris N. Khoromskij
Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. J. Comput. Phys. 334 (2017)
Venera Khoromskaia, Boris N. Khoromskij
Block Circulant and Toeplitz Structures in the Linearized Hartree-Fock Equation on Finite Lattices: Tensor Approach. Comput. Methods Appl. Math. 17 (3) (2017)
Venera Khoromskaia, Boris N. Khoromskij
Fast tensor method for summation of long-range potentials on 3D lattices with defects. Numer. Linear Algebra Appl. 23 (2) (2016)
Simon Etter, Sergey Dolgov, Boris N. Khoromskij
Erratum: Two-Level QTT-Tucker Format for Optimized Tensor Calculus. SIAM J. Matrix Anal. Appl. 37 (2) (2016)
Boris N. Khoromskij, Alexander Veit
Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation. Comput. Methods Appl. Math. 16 (1) (2016)
Sergey Dolgov, Boris N. Khoromskij
Simultaneous state-time approximation of the chemical master equation using tensor product formats. Numer. Linear Algebra Appl. 22 (2) (2015)
Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko, Hermann G. Matthies
Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format. SIAM/ASA J. Uncertain. Quantification 3 (1) (2015)
Sergey V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets, Dmitry V. Savostyanov
Computation of extreme eigenvalues in higher dimensions using block tensor train format. Comput. Phys. Commun. 185 (4) (2014)
Angelos Mantzaflaris, Bert Jüttler, Boris N. Khoromskij, Ulrich Langer
Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation. Curves and Surfaces (2014)
Boris N. Khoromskij, Sentao Miao
Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets. Comput. Methods Appl. Math. 14 (4) (2014)
Venera Khoromskaia, Boris N. Khoromskij
Møller-Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals. Comput. Phys. Commun. 185 (1) (2014)
Venera Khoromskaia, Boris N. Khoromskij
Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation. Comput. Phys. Commun. 185 (12) (2014)
Venera Khoromskaia, Boris N. Khoromskij, Reinhold Schneider
Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis. SIAM J. Sci. Comput. 35 (2) (2013)
Vladimir A. Kazeev, Boris N. Khoromskij, Eugene E. Tyrtyshnikov
Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity. SIAM J. Sci. Comput. 35 (3) (2013)
Sergey Dolgov, Boris N. Khoromskij
Two-Level QTT-Tucker Format for Optimized Tensor Calculus. SIAM J. Matrix Anal. Appl. 34 (2) (2013)
Sergey V. Dolgov, Boris N. Khoromskij, Ivan V. Oseledets
Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker-Planck Equation. SIAM J. Sci. Comput. 34 (6) (2012)
Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter, Eugene E. Tyrtyshnikov
Use of tensor formats in elliptic eigenvalue problems. Numer. Linear Algebra Appl. 19 (1) (2012)
Venera Khoromskaia, Dirk Andrae, Boris N. Khoromskij
Fast and accurate 3D tensor calculation of the Fock operator in a general basis. Comput. Phys. Commun. 183 (11) (2012)
Cristóbal Bertoglio, Boris N. Khoromskij
Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels. Comput. Phys. Commun. 183 (4) (2012)
Vladimir A. Kazeev, Boris N. Khoromskij
Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse. SIAM J. Matrix Anal. Appl. 33 (3) (2012)
Boris N. Khoromskij, Christoph Schwab
Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Sci. Comput. 33 (1) (2011)
Ivan P. Gavrilyuk, Boris N. Khoromskij, Eugene E. Tyrtyshnikov
Preface to the special issue, CMAM 2011, no. 3. Comput. Methods Appl. Math. 11 (3) (2011)
Venera Khoromskaia, Boris N. Khoromskij, Reinhold Schneider
QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations. Comput. Methods Appl. Math. 11 (3) (2011)
Ivan P. Gavrilyuk, Boris N. Khoromskij
Quantized-TT-Cayley Transform for Computing the Dynamics and the Spectrum of High-Dimensional Hamiltonians. Comput. Methods Appl. Math. 11 (3) (2011)
Boris N. Khoromskij, Venera Khoromskaia, Heinz-Jürgen Flad
Numerical Solution of the Hartree - Fock Equation in Multilevel Tensor-Structured Format. SIAM J. Sci. Comput. 33 (1) (2011)
Boris N. Khoromskij, Stefan A. Sauter, Alexander Veit
Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation. Comput. Methods Appl. Math. 11 (3) (2011)
Boris N. Khoromskij, Ivan V. Oseledets
Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs. Comput. Methods Appl. Math. 10 (4) (2010)
Boris N. Khoromskij
Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension. J. Comput. Appl. Math. 234 (11) (2010)
Boris N. Khoromskij, Venera Khoromskaia, Sambasiva Rao Chinnamsetty, Heinz-Jürgen Flad
Tensor decomposition in electronic structure calculations on 3D Cartesian grids. J. Comput. Phys. 228 (16) (2009)
Boris N. Khoromskij, Alexander Litvinenko, Hermann G. Matthies
Application of hierarchical matrices for computing the Karhunen-Loève expansion. Computing 84 (1-2) (2009)
Boris N. Khoromskij, Venera Khoromskaia
Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays. SIAM J. Sci. Comput. 31 (4) (2009)
Wolfgang Hackbusch, Boris N. Khoromskij, Eugene E. Tyrtyshnikov
Approximate iterations for structured matrices. Numerische Mathematik 109 (3) (2008)
Wolfgang Hackbusch, Boris N. Khoromskij
Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions. SIAM J. Matrix Anal. Appl. 30 (3) (2008)
Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter
Adaptive Galerkin boundary element methods with panel clustering. Numerische Mathematik 105 (4) (2007)
Wolfgang Hackbusch, Boris N. Khoromskij
Tensor-product approximation to operators and functions in high dimensions. J. Complex. 23 (4-6) (2007)
Maxim V. Fedorov, Heinz-Jürgen Flad, Gennady N. Chuev, Lars Grasedyck, Boris N. Khoromskij
A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. Computing 80 (1) (2007)
Boris N. Khoromskij
Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation. Math. Comput. 76 (259) (2007)
Wolfgang Hackbusch, Boris N. Khoromskij
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators. Computing 76 (3-4) (2006)
Wolfgang Hackbusch, Boris N. Khoromskij
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions. Computing 76 (3-4) (2006)
Wolfgang Hackbusch, Boris N. Khoromskij, Eugene E. Tyrtyshnikov
Hierarchical Kronecker tensor-product approximations. J. Num. Math. 13 (2) (2005)
Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij
Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High-Dimensional Elliptic Problems. Computing 74 (2) (2005)
Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij
Data-sparse approximation to a class of operator-valued functions. Math. Comput. 74 (250) (2005)
Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij
Data-sparse approximation to the operator-valued functions of elliptic operator. Math. Comput. 73 (247) (2004)
Wolfgang Hackbusch, Boris N. Khoromskij, Ronald Kriemann
Hierarchical Matrices Based on a Weak Admissibility Criterion. Computing 73 (3) (2004)
Lars Grasedyck, Wolfgang Hackbusch, Boris N. Khoromskij
Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices. Computing 70 (2) (2003)
Boris N. Khoromskij, Jens Markus Melenk
Boundary Concentrated Finite Element Methods. SIAM J. Numer. Anal. 41 (1) (2003)
Boris N. Khoromskij
Data-sparse elliptic operator inverse based on explicit approximation to the Green function. J. Num. Math. 11 (2) (2003)
Boris N. Khoromskij
Hierarchical matrix approximation to Green's function via boundary concentrated FEM. J. Num. Math. 11 (3) (2003)
Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij
ℋ-Matrix approximation for the operator exponential with applications. Numerische Mathematik 92 (1) (2002)
Wolfgang Hackbusch, Boris N. Khoromskij
Blended kernel approximation in the ℋ-matrix techniques. Numer. Linear Algebra Appl. 9 (4) (2002)
Boris N. Khoromskij, Jens Markus Melenk
An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. Computing 69 (2) (2002)
Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij
ℋ-matrix approximation for elliptic solution operators in cylinder domains. J. Num. Math. 9 (1) (2001)
Wolfgang Hackbusch, Boris N. Khoromskij
A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems. Computing 64 (1) (2000)
Boris N. Khoromskij, G. E. Mazurkevich, Gabriel Wittum
Frequency Filtering for Elliptic Interface Problems with Lagrange Multipliers. SIAM J. Sci. Comput. 21 (2) (1999)
Boris N. Khoromskij, Gabriel Wittum
An asymptotically optimal Schur complement reduction for the Stokes equation. Numerische Mathematik 81 (3) (1999)
Boris N. Khoromskij, Gabriel Wittum
Robust Schur complement method for strongly anisotropic elliptic equations. Numer. Linear Algebra Appl. 6 (8) (1999)
Boris N. Khoromskij, Siegfried Prössdorf
Fast computations with the harmonic Poincaré-Steklov operators on nested refined meshes. Adv. Comput. Math. 8 (1-2) (1998)
Boris N. Khoromskij
On Fast Computations with the Inverse to Harmonic Potential Operators via Domain Decomposition. Numer. Linear Algebra Appl. 3 (2) (1996)
Boris N. Khoromskij, Siegfried Prössdorf
Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation. Adv. Comput. Math. 4 (1) (1995)