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ORCIDBoris N. Khoromskij
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2020 – today
- 2023
[j74]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)- [j73]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) - 2022
- [j72]Venera Khoromskaia, Boris N. Khoromskij:
Ubiquitous Nature of the Reduced Higher Order SVD in Tensor-Based Scientific Computing. Frontiers Appl. Math. Stat. 8: 826988 (2022) - [j71]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) - [i6]Venera Khoromskaia, Boris N. Khoromskij:
Reduced Higher Order SVD: ubiquitous rank-reduction method in tensor-based scientific computing. CoRR abs/2201.12663 (2022) - 2021
- [j70]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: 109865 (2021) - [j69]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): A415-A445 (2021) - [i5]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 abs/2105.13206 (2021) - [i4]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 abs/2109.14073 (2021) - 2020
- [j68]Boris N. Khoromskij:
Range-separated tensor decomposition of the discretized Dirac delta and elliptic operator inverse. J. Comput. Phys. 401 (2020) - [j67]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) - [i3]Venera Khoromskaia, Boris N. Khoromskij:
Prospects of tensor-based numerical modeling of the collective electrostatic potential in many-particle systems. CoRR abs/2001.11393 (2020) - [i2]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 abs/2006.09314 (2020) - [i1]Venera Khoromskaia, Boris N. Khoromskij:
Tensor-based techniques for fast discretization and solution of 3D elliptic equations with random coefficients. CoRR abs/2007.06524 (2020)
2010 – 2019
- 2019
- [j66]Ivan P. Gavrilyuk, Boris N. Khoromskij:
Tensor Numerical Methods: Actual Theory and Recent Applications. Comput. Methods Appl. Math. 19(1): 1-4 (2019) - [j65]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): 55-71 (2019) - [j64]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): 101-122 (2019) - [j63]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: 221-239 (2019) - [j62]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) - 2018
- [j61]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: 136-155 (2018) - [j60]Peter Benner, Venera Khoromskaia, Boris N. Khoromskij:
Range-Separated Tensor Format for Many-Particle Modeling. SIAM J. Sci. Comput. 40(2) (2018) - 2017
- [j59]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): 431 (2017) - [j58]Boris N. Khoromskij, Sergey I. Repin:
Rank Structured Approximation Method for Quasi-Periodic Elliptic Problems. Comput. Methods Appl. Math. 17(3): 457 (2017) - [j57]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: 221-239 (2017) - 2016
- [j56]Boris N. Khoromskij, Alexander Veit:
Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation. Comput. Methods Appl. Math. 16(1): 145-159 (2016) - [j55]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): 249-271 (2016) - [j54]Simon Etter, Sergey Dolgov, Boris N. Khoromskij:
Erratum: Two-Level QTT-Tucker Format for Optimized Tensor Calculus. SIAM J. Matrix Anal. Appl. 37(2): 818-822 (2016) - 2015
- [j53]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): 1109-1135 (2015) - [j52]Sergey Dolgov, Boris N. Khoromskij:
Simultaneous state-time approximation of the chemical master equation using tensor product formats. Numer. Linear Algebra Appl. 22(2): 197-219 (2015) - 2014
- [j51]Boris N. Khoromskij, Sentao Miao:
Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets. Comput. Methods Appl. Math. 14(4): 537-553 (2014) - [j50]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): 2-10 (2014) - [j49]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): 1207-1216 (2014) - [j48]Venera Khoromskaia, Boris N. Khoromskij:
Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation. Comput. Phys. Commun. 185(12): 3162-3174 (2014) - [c1]Angelos Mantzaflaris, Bert Jüttler, Boris N. Khoromskij, Ulrich Langer:
Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation. Curves and Surfaces 2014: 321-340 - 2013
- [j47]Sergey Dolgov, Boris N. Khoromskij:
Two-Level QTT-Tucker Format for Optimized Tensor Calculus. SIAM J. Matrix Anal. Appl. 34(2): 593-623 (2013) - [j46]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) - [j45]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) - 2012
- [j44]Cristóbal Bertoglio, Boris N. Khoromskij:
Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels. Comput. Phys. Commun. 183(4): 904-912 (2012) - [j43]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): 2392-2404 (2012) - [j42]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): 133-151 (2012) - [j41]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): 742-758 (2012) - [j40]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) - 2011
- [j39]Ivan P. Gavrilyuk, Boris N. Khoromskij, Eugene E. Tyrtyshnikov:
Preface to the special issue, CMAM 2011, no. 3. Comput. Methods Appl. Math. 11(3): 272 (2011) - [j38]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): 273-290 (2011) - [j37]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): 327-341 (2011) - [j36]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): 342-362 (2011) - [j35]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): 45-65 (2011) - [j34]Boris N. Khoromskij, Christoph Schwab:
Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Sci. Comput. 33(1): 364-385 (2011) - 2010
- [j33]Boris N. Khoromskij, Ivan V. Oseledets:
Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs. Comput. Methods Appl. Math. 10(4): 376-394 (2010) - [j32]Boris N. Khoromskij:
Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension. J. Comput. Appl. Math. 234(11): 3122-3139 (2010)
2000 – 2009
- 2009
- [j31]Boris N. Khoromskij, Alexander Litvinenko, Hermann G. Matthies:
Application of hierarchical matrices for computing the Karhunen-Loève expansion. Computing 84(1-2): 49-67 (2009) - [j30]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): 5749-5762 (2009) - [j29]Boris N. Khoromskij, Venera Khoromskaia:
Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays. SIAM J. Sci. Comput. 31(4): 3002-3026 (2009) - 2008
- [j28]Wolfgang Hackbusch, Boris N. Khoromskij, Eugene E. Tyrtyshnikov:
Approximate iterations for structured matrices. Numerische Mathematik 109(3): 365-383 (2008) - [j27]Wolfgang Hackbusch, Boris N. Khoromskij:
Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions. SIAM J. Matrix Anal. Appl. 30(3): 1233-1253 (2008) - 2007
- [j26]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): 47-73 (2007) - [j25]Wolfgang Hackbusch, Boris N. Khoromskij:
Tensor-product approximation to operators and functions in high dimensions. J. Complex. 23(4-6): 697-714 (2007) - [j24]Boris N. Khoromskij:
Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation. Math. Comput. 76(259): 1291-1315 (2007) - [j23]Wolfgang Hackbusch, Boris N. Khoromskij, Stefan A. Sauter:
Adaptive Galerkin boundary element methods with panel clustering. Numerische Mathematik 105(4): 603-631 (2007) - 2006
- [j22]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): 177-202 (2006) - [j21]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): 203-225 (2006) - 2005
- [j20]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): 131-157 (2005) - [j19]Wolfgang Hackbusch, Boris N. Khoromskij, Eugene E. Tyrtyshnikov:
Hierarchical Kronecker tensor-product approximations. J. Num. Math. 13(2): 119-156 (2005) - [j18]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
Data-sparse approximation to a class of operator-valued functions. Math. Comput. 74(250): 681-708 (2005) - 2004
- [b1]Boris N. Khoromskij, Gabriel Wittum:
Numerical Solution of Elliptic Differential Equations by Reduction to the Interface. Lecture Notes in Computational Science and Engineering 36, Springer 2004, ISBN 978-3-540-20406-0, pp. I-XI, 1-299 - [j17]Wolfgang Hackbusch, Boris N. Khoromskij, Ronald Kriemann:
Hierarchical Matrices Based on a Weak Admissibility Criterion. Computing 73(3): 207-243 (2004) - [j16]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
Data-sparse approximation to the operator-valued functions of elliptic operator. Math. Comput. 73(247): 1297-1324 (2004) - 2003
- [j15]Lars Grasedyck, Wolfgang Hackbusch, Boris N. Khoromskij:
Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices. Computing 70(2): 121-165 (2003) - [j14]Boris N. Khoromskij:
Data-sparse elliptic operator inverse based on explicit approximation to the Green function. J. Num. Math. 11(2): 135-162 (2003) - [j13]Boris N. Khoromskij:
Hierarchical matrix approximation to Green's function via boundary concentrated FEM. J. Num. Math. 11(3): 195-223 (2003) - [j12]Boris N. Khoromskij, Jens Markus Melenk:
Boundary Concentrated Finite Element Methods. SIAM J. Numer. Anal. 41(1): 1-36 (2003) - 2002
- [j11]Boris N. Khoromskij, Jens Markus Melenk:
An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. Computing 69(2): 91-117 (2002) - [j10]Wolfgang Hackbusch, Boris N. Khoromskij:
Blended kernel approximation in the ℋ-matrix techniques. Numer. Linear Algebra Appl. 9(4): 281-304 (2002) - [j9]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
ℋ-Matrix approximation for the operator exponential with applications. Numerische Mathematik 92(1): 83-111 (2002) - 2001
- [j8]Ivan P. Gavrilyuk, Wolfgang Hackbusch, Boris N. Khoromskij:
ℋ-matrix approximation for elliptic solution operators in cylinder domains. J. Num. Math. 9(1): 25-58 (2001) - 2000
- [j7]Wolfgang Hackbusch, Boris N. Khoromskij:
A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems. Computing 64(1): 21-47 (2000)
1990 – 1999
- 1999
- [j6]Boris N. Khoromskij, Gabriel Wittum:
Robust Schur complement method for strongly anisotropic elliptic equations. Numer. Linear Algebra Appl. 6(8): 621-653 (1999) - [j5]Boris N. Khoromskij, Gabriel Wittum:
An asymptotically optimal Schur complement reduction for the Stokes equation. Numerische Mathematik 81(3): 345-375 (1999) - [j4]Boris N. Khoromskij, G. E. Mazurkevich, Gabriel Wittum:
Frequency Filtering for Elliptic Interface Problems with Lagrange Multipliers. SIAM J. Sci. Comput. 21(2): 421-440 (1999) - 1998
- [j3]Boris N. Khoromskij, Siegfried Prössdorf:
Fast computations with the harmonic Poincaré-Steklov operators on nested refined meshes. Adv. Comput. Math. 8(1-2): 111-135 (1998) - 1996
- [j2]Boris N. Khoromskij:
On Fast Computations with the Inverse to Harmonic Potential Operators via Domain Decomposition. Numer. Linear Algebra Appl. 3(2): 91-111 (1996) - 1995
- [j1]Boris N. Khoromskij, Siegfried Prössdorf:
Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation. Adv. Comput. Math. 4(1): 331-355 (1995)
Coauthor Index
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