Edit Profile (opens in new tab) Khoromskiĭ, Boris Nikolaevich Co-Author Distance Author ID: khoromskii.boris-n Published as: Khoromskij, Boris N.; Khoromskij, B. N.; Khoromskij, Boris; Khoromsky, B. N.; Khoronskij, Boris N.; Khoromskii, B. N.; Khoromskij, B. more...less Homepage: https://personal-homepages.mis.mpg.de/bokh/ External Links: Google Scholar · Math-Net.Ru · dblp · GND Documents Indexed: 128 Publications since 1976, including 3 Books 2 Contributions as Editor Co-Authors: 60 Co-Authors with 114 Joint Publications 2,063 Co-Co-Authors all top 5 Co-Authors 16 single-authored 24 Hackbusch, Wolfgang 23 Khoromskaia, Venera 13 Zhidkov, Eugeni P. 11 Dolgov, Sergey V. 9 Gavrilyuk, Ivan P. 8 Tyrtyshnikov, Evgeniĭ Evgen’evich 8 Wittum, Gabriel 6 Mazurkevich, G. E. 6 Oseledets, Ivan Valer’evich 5 Flad, Heinz-Jürgen 5 Litvinenko, Alexander 4 Benner, Peter 4 Sauter, Stefan 3 Kazeev, Vladimir A. 3 Kriemann, Ronald 3 Matthies, Hermann Georg 3 Savostyanov, Dmitry V. 3 Schmidt, Gunther 3 Schneider, Reinhold 3 Yamaleev, Robert M. 2 Gareev, Fangil A. 2 Goncharov, S. A. 2 Grasedyck, Lars 2 Jüttler, Bert 2 Langer, Ulrich 2 Mantzaflaris, Angelos 2 Melenk, Jens Markus 2 Nedyalkov, I. P. 2 Nikonov, Eh. G. 2 Prössdorf, Siegfried 2 Puzynin, Igor V. 2 Repin, Sergeĭ Igorevich 2 Schulz, Volker H. 2 Veit, Alexander 2 Wendland, Wolfgang L. 1 Akishin, Pavel G. 1 Amirkhanov, Ilkizar Valer’evich 1 Andrae, Dirk 1 Bertoglio, Cristóbal 1 Chinnamsetty, Sambasiva Rao 1 Chuev, Gennady N. 1 Etter, Simon 1 Fedorov, Maxim V. 1 Hebeker, Friedrich-Karl 1 Heidel, Gennadij 1 Hsiao, George Chia-Chu 1 Keyes, David Elliot 1 Kumar, N. Kishore 1 Kweyu, Cleophas M. 1 Miao, Sentao 1 Ngen, M. 1 Nguen, M. Kh. 1 Otto, Felix 1 Schmitt, Britta 1 Schneider, Jan 1 Schwab, Christoph 1 Stein, Matthias 1 Yang, Chao 1 Yudin, I. P. 1 Zhidkova, I. E. all top 5 Serials 13 Computational Methods in Applied Mathematics 11 Numerical Linear Algebra with Applications 9 Computing 9 SIAM Journal on Scientific Computing 6 Numerische Mathematik 5 Computer Physics Communications 5 Journal of Computational Physics 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 SIAM Journal on Matrix Analysis and Applications 4 U.S.S.R. Computational Mathematics and Mathematical Physics 3 Mathematics of Computation 3 East-West Journal of Numerical Mathematics 3 Russian Journal of Numerical Analysis and Mathematical Modelling 3 Journal of Numerical Mathematics 2 Journal of Computational and Applied Mathematics 2 Constructive Approximation 2 Soviet Journal of Numerical Analysis and Mathematical Modelling 2 Advances in Computational Mathematics 2 Computing and Visualization in Science 2 Matematicheskoe Modelirovanie 1 Computer Methods in Applied Mechanics and Engineering 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Differential Equations 1 Mathematics and Computers in Simulation 1 SIAM Journal on Numerical Analysis 1 Soviet Mathematics. Doklady 1 Journal of Computational Mathematics 1 Journal of Complexity 1 Journal of Integral Equations and Applications 1 Computational Mathematics and Mathematical Physics 1 Linear Algebra and its Applications 1 SIAM Review 1 Vychislitel’nye Protsessy i Sistemy 1 Siberian Journal of Computer Mathematics 1 Engineering Analysis with Boundary Elements 1 The Journal of Fourier Analysis and Applications 1 Central European Journal of Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Radon Series on Computational and Applied Mathematics 1 SIAM/ASA Journal on Uncertainty Quantification 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys all top 5 Fields 121 Numerical analysis (65-XX) 52 Partial differential equations (35-XX) 27 Linear and multilinear algebra; matrix theory (15-XX) 14 Integral equations (45-XX) 11 Quantum theory (81-XX) 9 Operator theory (47-XX) 9 Optics, electromagnetic theory (78-XX) 6 Functional analysis (46-XX) 5 Probability theory and stochastic processes (60-XX) 4 General and overarching topics; collections (00-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Special functions (33-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 1,807 times in 765 Documents Cited by ▼ Year ▼ A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems. Zbl 0962.65029Hackbusch, W.; Khoromskij, B. N. 132 2000 \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling. Zbl 1228.65069Khoromskij, Boris N. 90 2011 Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. Zbl 1243.65009Khoromskij, Boris N.; Schwab, Christoph 77 2011 On \({\mathcal H}^2\)-matrices. Zbl 0963.65043Hackbusch, W.; Khoromskij, B.; Sauter, S. A. 65 2000 Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions. Zbl 1087.65049Hackbusch, W.; Khoromskij, B. N. 56 2006 Multigrid accelerated tensor approximation of function related multidimensional arrays. Zbl 1197.65215Khoromskij, B. N.; Khoromskaia, V. 50 2009 Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Zbl 1071.65032Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 49 2005 Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Zbl 1239.65026Grasedyck, Lars; Hackbusch, Wolfgang; Khoromskij, B. N. 46 2003 Approximate iterations for structured matrices. Zbl 1144.65029Hackbusch, Wolfgang; Khoromskij, Boris N.; Tyrtyshnikov, Eugene E. 44 2008 Fast solution of parabolic problems in the tensor train/quantized tensor train format with initial application to the Fokker-Planck equation. Zbl 1259.82075Dolgov, S. V.; Khoromskij, B. N.; Oseledets, I. V. 44 2012 Hierarchical Kronecker tensor-product approximations. Zbl 1081.65035Hackbusch, W.; Khoromskij, B. N.; Tyrtyshnikov, E. E. 43 2005 Low-rank explicit QTT representation of the Laplace operator and its inverse. Zbl 1268.15025Kazeev, Vladimir A.; Khoromskij, Boris N. 40 2012 Hierarchical matrices based on a weak admissibility criterion. Zbl 1063.65035Hackbusch, W.; Khoromskij, B. N.; Kriemann, R. 40 2004 Polynomial chaos expansion of random coefficients and the solution of stochastic partial differential equations in the tensor train format. Zbl 1329.65271Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G. 36 2015 Low rank tensor methods in Galerkin-based isogeometric analysis. Zbl 1439.65185Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, Boris N.; Langer, Ulrich 35 2017 Structured rank-\((r_1, \dots , r_d)\) decomposition of function-related tensors in \(\mathbb R^d\). Zbl 1120.65052Khoromskij, B. N. 34 2006 A sparse \({\mathcal H}\)-matrix arithmetic: General complexity estimates. Zbl 0977.65036Hackbusch, W.; Khoromskij, B. N. 32 2000 Computation of extreme eigenvalues in higher dimensions using block tensor train format. Zbl 1344.65043Dolgov, S. V.; Khoromskij, B. N.; Oseledets, I. V.; Savostyanov, D. V. 31 2014 Tensor numerical methods in scientific computing. Zbl 1405.65002Khoromskij, Boris N. 31 2018 Tensor-structured preconditioners and approximate inverse of elliptic operators in \(\mathbb R^{d}\). Zbl 1185.65051Khoromskij, Boris N. 31 2009 Data-sparse approximation to a class of operator-valued functions. Zbl 1066.65060Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 31 2005 Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs. Zbl 1283.65039Khoromskij, B. N.; Oseledets, I. 31 2010 Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity. Zbl 1275.15018Kazeev, Vladimir A.; Khoromskij, Boris N.; Tyrtyshnikov, Eugene E. 30 2013 Data-sparse approximation to the operator-valued functions of elliptic operator. Zbl 1065.47009Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 30 2004 Application of hierarchical matrices for computing the Karhunen-Loève expansion. Zbl 1162.65306Khoromskij, B. N.; Litvinenko, A.; Matthies, H. G. 29 2009 \(\mathcal H\)-matrix approximation for the operator exponential with applications. Zbl 1005.65113Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 28 2002 Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension. Zbl 1197.65216Khoromskij, Boris N. 27 2010 Low rank Tucker-type tensor approximation to classical potentials. Zbl 1130.65060Khoromskij, B. N.; Khoromskaia, V. 27 2007 Tensor-product approximation to operators and functions in high dimensions. Zbl 1141.65032Hackbusch, Wolfgang; Khoromskij, Boris N. 27 2007 Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format. Zbl 1227.65113Khoromskij, B. N.; Khoromskaia, V.; Flad, H.-J. 27 2011 Tensor numerical methods for multidimensional PDEs: theoretical analysis and initial applications. Zbl 1382.65461Khoromskij, Boris N. 25 2015 Superfast Fourier transform using QTT approximation. Zbl 1260.65114Dolgov, Sergey; Khoromskij, Boris; Savostyanov, Dmitry 23 2012 Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators. Zbl 1087.65050Hackbusch, W.; Khoromskij, B. N. 22 2006 QTT approximation of elliptic solution operators in higher dimensions. Zbl 1221.65288Khoromskij, B. N.; Oseledets, I. V. 21 2011 Two-level QTT-Tucker format for optimized tensor calculus. Zbl 1273.65169Dolgov, Sergey; Khoromskij, Boris 20 2013 Simultaneous state-time approximation of the chemical master equation using tensor product formats. Zbl 1363.65117Dolgov, Sergey; Khoromskij, Boris 20 2015 Use of tensor formats in elliptic eigenvalue problems. Zbl 1274.35252Hackbusch, Wolfgang; Khoromskij, Boris N.; Sauter, Stefan; Tyrtyshnikov, Eugene E. 19 2012 Boundary concentrated finite element methods. Zbl 1050.65113Khoromskij, B. N.; Melenk, J. M. 19 2003 Tensor-structured factorized calculation of two-electron integrals in a general basis. Zbl 1266.65069Khoromskaia, V.; Khoromskij, B. N.; Schneider, R. 18 2013 Matrix generation in isogeometric analysis by low rank tensor approximation. Zbl 1360.65282Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, B. N.; Langer, Ulrich 18 2015 Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels. Zbl 1308.65213Bertoglio, Cristóbal; Khoromskij, Boris N. 17 2012 Tensor decomposition in electronic structure calculations on 3D Cartesian grids. Zbl 1171.82017Khoromskij, B. N.; Khoromskaia, V.; Chinnamsetty, S. R.; Flad, H.-J. 16 2009 Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation. Zbl 1360.78016Khoromskaia, Venera; Khoromskij, Boris N. 16 2014 Numerical solution of elliptic differential equations by reduction to the interface. Zbl 1043.65128Khoromskij, Boris N.; Wittum, Gabriel 15 2004 Range-separated tensor format for many-particle modeling. Zbl 1446.65202Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N. 14 2018 Tensor numerical methods in quantum chemistry. Zbl 1503.65003Khoromskaia, Venera; Khoromskij, Boris N. 14 2018 Verification of the cross 3D algorithm on quantum chemistry data. Zbl 1147.81317Flad, H.-J.; Khoromskii, B. N.; Savostyanov, D. V.; Tyrtyshnikov, E. E. 13 2008 Fast and accurate 3D tensor calculation of the Fock operator in a general basis. Zbl 1302.81009Khoromskaia, V.; Andrae, D.; Khoromskij, B. N. 10 2012 Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. Zbl 1376.65045Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N. 9 2017 Towards \(\mathcal H\)-matrix approximation of linear complexity. Zbl 1004.65125Hackbusch, Wolfgang; Khoromskij, Boris N. 9 2001 Fast tensor method for summation of long-range potentials on 3D lattices with defects. Zbl 1413.65141Khoromskaia, Venera; Khoromskij, Boris N. 8 2016 Quantized-TT-Cayley transform for computing the dynamics and the spectrum of high-dimensional Hamiltonians. Zbl 1283.65036Gavrilyuk, Ivan; Khoromskij, Boris 8 2011 QTT representation of the Hartree and exchange operators in electronic structure calculations. Zbl 1283.65038Khoromskaia, Venera; Khoromskij, Boris; Schneider, Reinhold 7 2011 Fast quadrature techniques for retarded potentials based on TT/QTT tensor approximation. Zbl 1283.65040Khoromskij, Boris; Sauter, Stefan; Veit, Alexander 7 2011 Tensor-product approximation to multidimensional integral operators and Green’s functions. Zbl 1171.65099Hackbusch, Wolfgang; Khoromskij, Boris N. 6 2008 Spectrally equivalent preconditioners for boundary equations in substructuring techniques. Zbl 0835.65131Khoromskij, B. N.; Wendland, Wolfgang L. 6 1993 Rank structured approximation method for quasi-periodic elliptic problems. Zbl 1380.65069Khoromskij, Boris; Repin, Sergey 6 2017 An efficient direct solver for the boundary concentrated FEM in 2D. Zbl 1017.65089Khoromskij, B. N.; Melenk, J. M. 6 2002 Preconditioning for boundary element methods in domain decomposition. Zbl 0988.65115Hsiao, G. C.; Khoromskij, B. N.; Wendland, W. L. 6 2001 \(\mathcal H\)-matrix approximation for elliptic solution operators in cylinder domains. Zbl 1012.65134Gavrilyuk, I. P.; Hackbusch, W.; Khoromskij, B. N. 6 2001 Range-separated tensor decomposition of the discretized Dirac delta and elliptic operator inverse. Zbl 1453.65035Khoromskij, Boris N. 5 2020 Møller-Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals. Zbl 1344.65035Khoromskaia, V.; Khoromskij, B. N. 5 2014 Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation. Zbl 1113.65040Khoromskij, Boris N. 5 2007 A fast iteration method for solving elliptic problems with quasiperiodic coefficients. Zbl 1328.65098Khoromskij, Boris N.; Repin, Sergey I. 5 2015 Regularization of Poisson-Boltzmann-type equations with singular source terms using the range-separated tensor format. Zbl 1466.65180Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris; Kweyu, Cleophas; Stein, Matthias 5 2021 Efficient computation of highly oscillatory integrals by using QTT tensor approximation. Zbl 1329.65088Khoromskij, Boris; Veit, Alexander 4 2016 Superfast wavelet transform using quantics-TT approximation. I: Application to Haar wavelets. Zbl 1304.65139Khoromskij, Boris N.; Miao, Sentao 4 2014 Concepts of data-sparse tensor-product approximation in many-particle modelling. Zbl 1214.81077Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Khoromskij, Boris N.; Schneider, Reinhold 4 2010 Data sparse computation of the Karhunen-Loève expansion. Zbl 1167.65326Khoromskij, B. N.; Litvinenko, A. 4 2008 Direct Schur complement method by domain decomposition based on \(H\)-matrix approximation. Zbl 1512.65292Hackbusch, Wolfgang; Khoromskij, Boris N.; Kriemann, Ronald 4 2005 Tucker tensor analysis of Matérn functions in spatial statistics. Zbl 1420.60084Litvinenko, Alexander; Keyes, David; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G. 4 2019 Boundary integral equations for the biharmonic Dirichlet problem on nonsmooth domains. Zbl 0974.65111Schmidt, Gunther; Khoromskij, Boris N. 4 1999 Robust interface reduction for highly anisotropic elliptic equations. Zbl 0926.65131Khoromskij, Boris N.; Wittum, Gabriel 4 1998 Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients. Zbl 1484.65326Dolgov, Sergey V.; Kazeev, Vladimir A.; Khoromskij, Boris N. 3 2018 A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. Zbl 1117.65170Fedorov, M. V.; Flad, H.-J.; Chuev, G. N.; Grasedyck, L.; Khoromskij, B. N. 3 2007 Low-rank tensor structure of solutions to elliptic problems with jumping coefficients. Zbl 1265.35053Dolgov, Sergey; Khoromskij, Boris N.; Oseledets, Ivan; Tyrtyshnikov, Eugene E. 3 2012 Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation. Zbl 0839.65129Khoromskij, Boris N.; Prößdorf, Siegfried 3 1995 On fast computations with the inverse to harmonic potential operators via domain decomposition. Zbl 0854.65107Khoromskij, Boris N. 3 1996 Quasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolation. Zbl 1420.65056Gavrilyuk, Ivan; Khoromskij, Boris N. 3 2019 Numerical study in stochastic homogenization for elliptic partial differential equations: convergence rate in the size of representative volume elements. Zbl 07217205Khoromskaia, Venera; Khoromskij, Boris N.; Otto, Felix 3 2020 Frequency filtering for elliptic interface problems with Lagrange multipliers. Zbl 0943.65076Khoromskij, B. N.; Mazurkevich, G. E.; Wittum, G. 3 1999 Direct Schur complement method by hierarchical matrix techniques. Zbl 1066.65143Hackbusch, Wolfgang; Khoromskij, Boris N.; Kriemann, Ronald 3 2005 Data-sparse elliptic operator inverse based on explicit approximation to the Green function. Zbl 1115.65376Khoromskij, B. N. 3 2003 Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints. Zbl 07508470Heidel, Gennadij; Khoromskaia, Venera; Khoromskij, Boris N.; Schulz, Volker 2 2021 Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach. Zbl 1380.65355Khoromskaia, Venera; Khoromskij, Boris N. 2 2017 Asymptotically optimal interface solvers for the biharmonic Dirichlet problem on convex polygonal domains. Zbl 0900.65319Khoromskij, B. N.; Schmidt, G. 2 1996 A fast interface solver for the biharmonic Dirichlet problem on polygonal domains. Zbl 0899.65066Khoromskij, B. N.; Schmidt, G. 2 1998 Hierarchical matrix approximation to Green’s function via boundary concentrated FEM. Zbl 1047.65103Khoromskij, B. N. 2 2003 Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation. Zbl 1451.65054Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N.; Yang, Chao 1 2019 A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients. Zbl 1247.65044Dolgov, Sergey; Khoromskij, Boris N.; Oseledets, Ivan; Tyrtyshnikov, Eugene 1 2012 Domain decomposition based \(\mathcal{H}\)-matrix preconditioners for the skin prolem. Zbl 1140.65370Khoromskij, Boris N.; Litvinenko, Alexander 1 2008 Domain decomposition method for magnetostatics nonlinear problems in combined formulation. Zbl 0816.65118Khoromsky, B. N.; Mazurkevich, G. E.; Zhidkov, E. P. 1 1990 Editorial. Tensor numerical methods: actual theory and recent applications. Zbl 1422.00020 1 2019 Preconditioners for one class of elliptic problems in not simply connected domains. Zbl 0770.65086Khoromskij, B. N.; Mazurkevich, G. E. 1 1992 Robust iterative methods for elliptic problems with highly varying coefficients in thin substructures. Zbl 0857.65033Khoromskij, B. N.; Wittum, G. 1 1996 Robust Schur complement method for strongly anisotropic elliptic equations. Zbl 0982.65133Khoromskij, Boris N.; Wittum, Gabriel 1 1999 An asymptotically optimal Schur complement reduction for the Stokes equation. Zbl 0947.76054Khoromskij, Boris N.; Wittum, Gabriel 1 1999 On a sparse finite element approximation to the Poincaré-Steklov operators of planar elasticity. Zbl 0914.73061Khoromskij, B. N. 1 1998 Blended kernel approximation in the \({\mathcal {H}}\)-matrix techniques. Zbl 1071.65553Hackbusch, W.; Khoromskij, B. N. 1 2002 Prospects of tensor-based numerical modeling of the collective electrostatics in many-particle systems. Zbl 1469.82010Khoromskaia, V.; Khoromskij, B. N. 1 2021 Regularization of Poisson-Boltzmann-type equations with singular source terms using the range-separated tensor format. Zbl 1466.65180Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris; Kweyu, Cleophas; Stein, Matthias 5 2021 Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints. Zbl 07508470Heidel, Gennadij; Khoromskaia, Venera; Khoromskij, Boris N.; Schulz, Volker 2 2021 Prospects of tensor-based numerical modeling of the collective electrostatics in many-particle systems. Zbl 1469.82010Khoromskaia, V.; Khoromskij, B. N. 1 2021 Range-separated tensor decomposition of the discretized Dirac delta and elliptic operator inverse. Zbl 1453.65035Khoromskij, Boris N. 5 2020 Numerical study in stochastic homogenization for elliptic partial differential equations: convergence rate in the size of representative volume elements. Zbl 07217205Khoromskaia, Venera; Khoromskij, Boris N.; Otto, Felix 3 2020 Tucker tensor analysis of Matérn functions in spatial statistics. Zbl 1420.60084Litvinenko, Alexander; Keyes, David; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G. 4 2019 Quasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolation. Zbl 1420.65056Gavrilyuk, Ivan; Khoromskij, Boris N. 3 2019 Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation. Zbl 1451.65054Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N.; Yang, Chao 1 2019 Editorial. Tensor numerical methods: actual theory and recent applications. Zbl 1422.00020 1 2019 Tensor numerical methods in scientific computing. Zbl 1405.65002Khoromskij, Boris N. 31 2018 Range-separated tensor format for many-particle modeling. Zbl 1446.65202Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N. 14 2018 Tensor numerical methods in quantum chemistry. Zbl 1503.65003Khoromskaia, Venera; Khoromskij, Boris N. 14 2018 Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients. Zbl 1484.65326Dolgov, Sergey V.; Kazeev, Vladimir A.; Khoromskij, Boris N. 3 2018 Low rank tensor methods in Galerkin-based isogeometric analysis. Zbl 1439.65185Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, Boris N.; Langer, Ulrich 35 2017 Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. Zbl 1376.65045Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N. 9 2017 Rank structured approximation method for quasi-periodic elliptic problems. Zbl 1380.65069Khoromskij, Boris; Repin, Sergey 6 2017 Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach. Zbl 1380.65355Khoromskaia, Venera; Khoromskij, Boris N. 2 2017 Fast tensor method for summation of long-range potentials on 3D lattices with defects. Zbl 1413.65141Khoromskaia, Venera; Khoromskij, Boris N. 8 2016 Efficient computation of highly oscillatory integrals by using QTT tensor approximation. Zbl 1329.65088Khoromskij, Boris; Veit, Alexander 4 2016 Polynomial chaos expansion of random coefficients and the solution of stochastic partial differential equations in the tensor train format. Zbl 1329.65271Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G. 36 2015 Tensor numerical methods for multidimensional PDEs: theoretical analysis and initial applications. Zbl 1382.65461Khoromskij, Boris N. 25 2015 Simultaneous state-time approximation of the chemical master equation using tensor product formats. Zbl 1363.65117Dolgov, Sergey; Khoromskij, Boris 20 2015 Matrix generation in isogeometric analysis by low rank tensor approximation. Zbl 1360.65282Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, B. N.; Langer, Ulrich 18 2015 A fast iteration method for solving elliptic problems with quasiperiodic coefficients. Zbl 1328.65098Khoromskij, Boris N.; Repin, Sergey I. 5 2015 Computation of extreme eigenvalues in higher dimensions using block tensor train format. Zbl 1344.65043Dolgov, S. V.; Khoromskij, B. N.; Oseledets, I. V.; Savostyanov, D. V. 31 2014 Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation. Zbl 1360.78016Khoromskaia, Venera; Khoromskij, Boris N. 16 2014 Møller-Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals. Zbl 1344.65035Khoromskaia, V.; Khoromskij, B. N. 5 2014 Superfast wavelet transform using quantics-TT approximation. I: Application to Haar wavelets. Zbl 1304.65139Khoromskij, Boris N.; Miao, Sentao 4 2014 Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity. Zbl 1275.15018Kazeev, Vladimir A.; Khoromskij, Boris N.; Tyrtyshnikov, Eugene E. 30 2013 Two-level QTT-Tucker format for optimized tensor calculus. Zbl 1273.65169Dolgov, Sergey; Khoromskij, Boris 20 2013 Tensor-structured factorized calculation of two-electron integrals in a general basis. Zbl 1266.65069Khoromskaia, V.; Khoromskij, B. N.; Schneider, R. 18 2013 Fast solution of parabolic problems in the tensor train/quantized tensor train format with initial application to the Fokker-Planck equation. Zbl 1259.82075Dolgov, S. V.; Khoromskij, B. N.; Oseledets, I. V. 44 2012 Low-rank explicit QTT representation of the Laplace operator and its inverse. Zbl 1268.15025Kazeev, Vladimir A.; Khoromskij, Boris N. 40 2012 Superfast Fourier transform using QTT approximation. Zbl 1260.65114Dolgov, Sergey; Khoromskij, Boris; Savostyanov, Dmitry 23 2012 Use of tensor formats in elliptic eigenvalue problems. Zbl 1274.35252Hackbusch, Wolfgang; Khoromskij, Boris N.; Sauter, Stefan; Tyrtyshnikov, Eugene E. 19 2012 Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels. Zbl 1308.65213Bertoglio, Cristóbal; Khoromskij, Boris N. 17 2012 Fast and accurate 3D tensor calculation of the Fock operator in a general basis. Zbl 1302.81009Khoromskaia, V.; Andrae, D.; Khoromskij, B. N. 10 2012 Low-rank tensor structure of solutions to elliptic problems with jumping coefficients. Zbl 1265.35053Dolgov, Sergey; Khoromskij, Boris N.; Oseledets, Ivan; Tyrtyshnikov, Eugene E. 3 2012 A reciprocal preconditioner for structured matrices arising from elliptic problems with jumping coefficients. Zbl 1247.65044Dolgov, Sergey; Khoromskij, Boris N.; Oseledets, Ivan; Tyrtyshnikov, Eugene 1 2012 \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling. Zbl 1228.65069Khoromskij, Boris N. 90 2011 Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. Zbl 1243.65009Khoromskij, Boris N.; Schwab, Christoph 77 2011 Numerical solution of the Hartree-Fock equation in multilevel tensor-structured format. Zbl 1227.65113Khoromskij, B. N.; Khoromskaia, V.; Flad, H.-J. 27 2011 QTT approximation of elliptic solution operators in higher dimensions. Zbl 1221.65288Khoromskij, B. N.; Oseledets, I. V. 21 2011 Quantized-TT-Cayley transform for computing the dynamics and the spectrum of high-dimensional Hamiltonians. Zbl 1283.65036Gavrilyuk, Ivan; Khoromskij, Boris 8 2011 QTT representation of the Hartree and exchange operators in electronic structure calculations. Zbl 1283.65038Khoromskaia, Venera; Khoromskij, Boris; Schneider, Reinhold 7 2011 Fast quadrature techniques for retarded potentials based on TT/QTT tensor approximation. Zbl 1283.65040Khoromskij, Boris; Sauter, Stefan; Veit, Alexander 7 2011 Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs. Zbl 1283.65039Khoromskij, B. N.; Oseledets, I. 31 2010 Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension. Zbl 1197.65216Khoromskij, Boris N. 27 2010 Concepts of data-sparse tensor-product approximation in many-particle modelling. Zbl 1214.81077Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Khoromskij, Boris N.; Schneider, Reinhold 4 2010 Multigrid accelerated tensor approximation of function related multidimensional arrays. Zbl 1197.65215Khoromskij, B. N.; Khoromskaia, V. 50 2009 Tensor-structured preconditioners and approximate inverse of elliptic operators in \(\mathbb R^{d}\). Zbl 1185.65051Khoromskij, Boris N. 31 2009 Application of hierarchical matrices for computing the Karhunen-Loève expansion. Zbl 1162.65306Khoromskij, B. N.; Litvinenko, A.; Matthies, H. G. 29 2009 Tensor decomposition in electronic structure calculations on 3D Cartesian grids. Zbl 1171.82017Khoromskij, B. N.; Khoromskaia, V.; Chinnamsetty, S. R.; Flad, H.-J. 16 2009 Approximate iterations for structured matrices. Zbl 1144.65029Hackbusch, Wolfgang; Khoromskij, Boris N.; Tyrtyshnikov, Eugene E. 44 2008 Verification of the cross 3D algorithm on quantum chemistry data. Zbl 1147.81317Flad, H.-J.; Khoromskii, B. N.; Savostyanov, D. V.; Tyrtyshnikov, E. E. 13 2008 Tensor-product approximation to multidimensional integral operators and Green’s functions. Zbl 1171.65099Hackbusch, Wolfgang; Khoromskij, Boris N. 6 2008 Data sparse computation of the Karhunen-Loève expansion. Zbl 1167.65326Khoromskij, B. N.; Litvinenko, A. 4 2008 Domain decomposition based \(\mathcal{H}\)-matrix preconditioners for the skin prolem. Zbl 1140.65370Khoromskij, Boris N.; Litvinenko, Alexander 1 2008 Low rank Tucker-type tensor approximation to classical potentials. Zbl 1130.65060Khoromskij, B. N.; Khoromskaia, V. 27 2007 Tensor-product approximation to operators and functions in high dimensions. Zbl 1141.65032Hackbusch, Wolfgang; Khoromskij, Boris N. 27 2007 Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation. Zbl 1113.65040Khoromskij, Boris N. 5 2007 A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. Zbl 1117.65170Fedorov, M. V.; Flad, H.-J.; Chuev, G. N.; Grasedyck, L.; Khoromskij, B. N. 3 2007 Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions. Zbl 1087.65049Hackbusch, W.; Khoromskij, B. N. 56 2006 Structured rank-\((r_1, \dots , r_d)\) decomposition of function-related tensors in \(\mathbb R^d\). Zbl 1120.65052Khoromskij, B. N. 34 2006 Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators. Zbl 1087.65050Hackbusch, W.; Khoromskij, B. N. 22 2006 Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Zbl 1071.65032Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 49 2005 Hierarchical Kronecker tensor-product approximations. Zbl 1081.65035Hackbusch, W.; Khoromskij, B. N.; Tyrtyshnikov, E. E. 43 2005 Data-sparse approximation to a class of operator-valued functions. Zbl 1066.65060Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 31 2005 Direct Schur complement method by domain decomposition based on \(H\)-matrix approximation. Zbl 1512.65292Hackbusch, Wolfgang; Khoromskij, Boris N.; Kriemann, Ronald 4 2005 Direct Schur complement method by hierarchical matrix techniques. Zbl 1066.65143Hackbusch, Wolfgang; Khoromskij, Boris N.; Kriemann, Ronald 3 2005 Hierarchical matrices based on a weak admissibility criterion. Zbl 1063.65035Hackbusch, W.; Khoromskij, B. N.; Kriemann, R. 40 2004 Data-sparse approximation to the operator-valued functions of elliptic operator. Zbl 1065.47009Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 30 2004 Numerical solution of elliptic differential equations by reduction to the interface. Zbl 1043.65128Khoromskij, Boris N.; Wittum, Gabriel 15 2004 Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Zbl 1239.65026Grasedyck, Lars; Hackbusch, Wolfgang; Khoromskij, B. N. 46 2003 Boundary concentrated finite element methods. Zbl 1050.65113Khoromskij, B. N.; Melenk, J. M. 19 2003 Data-sparse elliptic operator inverse based on explicit approximation to the Green function. Zbl 1115.65376Khoromskij, B. N. 3 2003 Hierarchical matrix approximation to Green’s function via boundary concentrated FEM. Zbl 1047.65103Khoromskij, B. N. 2 2003 \(\mathcal H\)-matrix approximation for the operator exponential with applications. Zbl 1005.65113Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. 28 2002 An efficient direct solver for the boundary concentrated FEM in 2D. Zbl 1017.65089Khoromskij, B. N.; Melenk, J. M. 6 2002 Blended kernel approximation in the \({\mathcal {H}}\)-matrix techniques. Zbl 1071.65553Hackbusch, W.; Khoromskij, B. N. 1 2002 Towards \(\mathcal H\)-matrix approximation of linear complexity. Zbl 1004.65125Hackbusch, Wolfgang; Khoromskij, Boris N. 9 2001 Preconditioning for boundary element methods in domain decomposition. Zbl 0988.65115Hsiao, G. C.; Khoromskij, B. N.; Wendland, W. L. 6 2001 \(\mathcal H\)-matrix approximation for elliptic solution operators in cylinder domains. Zbl 1012.65134Gavrilyuk, I. P.; Hackbusch, W.; Khoromskij, B. N. 6 2001 A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems. Zbl 0962.65029Hackbusch, W.; Khoromskij, B. N. 132 2000 On \({\mathcal H}^2\)-matrices. Zbl 0963.65043Hackbusch, W.; Khoromskij, B.; Sauter, S. A. 65 2000 A sparse \({\mathcal H}\)-matrix arithmetic: General complexity estimates. Zbl 0977.65036Hackbusch, W.; Khoromskij, B. N. 32 2000 \(\mathcal H\)-matrix approximation on graded meshes. Zbl 0960.65047Hackbusch, Wolfgang; Khoronskij, Boris N. 1 2000 Boundary integral equations for the biharmonic Dirichlet problem on nonsmooth domains. Zbl 0974.65111Schmidt, Gunther; Khoromskij, Boris N. 4 1999 Frequency filtering for elliptic interface problems with Lagrange multipliers. Zbl 0943.65076Khoromskij, B. N.; Mazurkevich, G. E.; Wittum, G. 3 1999 Robust Schur complement method for strongly anisotropic elliptic equations. Zbl 0982.65133Khoromskij, Boris N.; Wittum, Gabriel 1 1999 An asymptotically optimal Schur complement reduction for the Stokes equation. Zbl 0947.76054Khoromskij, Boris N.; Wittum, Gabriel 1 1999 Robust interface reduction for highly anisotropic elliptic equations. Zbl 0926.65131Khoromskij, Boris N.; Wittum, Gabriel 4 1998 A fast interface solver for the biharmonic Dirichlet problem on polygonal domains. Zbl 0899.65066Khoromskij, B. N.; Schmidt, G. 2 1998 On a sparse finite element approximation to the Poincaré-Steklov operators of planar elasticity. Zbl 0914.73061Khoromskij, B. N. 1 1998 On fast computations with the inverse to harmonic potential operators via domain decomposition. Zbl 0854.65107Khoromskij, Boris N. 3 1996 Asymptotically optimal interface solvers for the biharmonic Dirichlet problem on convex polygonal domains. Zbl 0900.65319Khoromskij, B. N.; Schmidt, G. 2 1996 Robust iterative methods for elliptic problems with highly varying coefficients in thin substructures. Zbl 0857.65033Khoromskij, B. N.; Wittum, G. 1 1996 Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation. Zbl 0839.65129Khoromskij, Boris N.; Prößdorf, Siegfried 3 1995 Spectrally equivalent preconditioners for boundary equations in substructuring techniques. Zbl 0835.65131Khoromskij, B. N.; Wendland, Wolfgang L. 6 1993 Preconditioners for one class of elliptic problems in not simply connected domains. Zbl 0770.65086Khoromskij, B. N.; Mazurkevich, G. E. 1 1992 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,033 Authors 50 Khoromskiĭ, Boris Nikolaevich 36 Hackbusch, Wolfgang 24 Oseledets, Ivan Valer’evich 23 Dolgov, Sergey V. 23 Kressner, Daniel 19 Benner, Peter 18 Börm, Steffen 18 Tyrtyshnikov, Evgeniĭ Evgen’evich 16 Bebendorf, Mario 15 Grasedyck, Lars 15 Matthies, Hermann Georg 14 Khoromskaia, Venera 14 Schneider, Reinhold 14 Ying, Lexing 13 Harbrecht, Helmut 12 Darve, Eric 12 Gavrilyuk, Ivan P. 12 Schwab, Christoph 11 Litvinenko, Alexander 11 Melenk, Jens Markus 11 Savostyanov, Dmitry V. 11 Schmidt, Gunther 10 Bachmayr, Markus 10 Jüttler, Bert 10 Lanzara, Flavia 10 Nouy, Anthony 10 Rakhuba, Maxim V. 10 Simoncini, Valeria 9 Makarov, Volodymyr Leonidovych 9 Uschmajew, André 8 Espig, Mike 8 Maz’ya, Vladimir Gilelevich 8 Tani, Mattia 8 Xia, Jianlin 7 Ho, Kenneth L. 7 Kazeev, Vladimir A. 7 Keyes, David Elliot 7 Lin, Lin 7 Sangalli, Giancarlo 7 Sauter, Stefan 7 Venturi, Daniele 6 Ballani, Jonas 6 Ehrlacher, Virginie 6 Eigel, Martin 6 Mantzaflaris, Angelos 6 Massei, Stefano 6 Multerer, Michael D. 5 Chow, Edmond 5 Dahmen, Wolfgang A. 5 Dektor, Alec 5 Dölz, Jürgen 5 Doostan, Alireza 5 Faustmann, Markus 5 Huang, Jingfang 5 Li, Xiaoye Sherry 5 Martinsson, Per-Gunnar 5 Stoll, Martin 5 Vabishchevich, Pëtr Nikolaevich 5 Vandereycken, Bart 5 Xi, Yuanzhe 5 Xing, Xin 4 Ferri Aliabadi, Mohammad Hossien 4 Ambikasaran, Sivaram 4 Baur, Ulrike 4 Benedetti, Ivano 4 Cichocki, Andrzej 4 De Lathauwer, Lieven 4 Exl, Lukas 4 Flad, Heinz-Jürgen 4 Gelß, Patrick 4 Kriemann, Ronald 4 Langer, Ulrich 4 Lee, Namgil 4 Lombardi, Damiano 4 Mach, Thomas 4 Palitta, Davide 4 Pan, Maodong 4 Pfeffer, Max 4 Praetorius, Dirk 4 Robol, Leonardo 4 Rodgers, Abram 4 Rosić, Bojana V. 4 Saad, Yousef 4 Scheichl, Robert 4 Schulz, Volker H. 4 Tobler, Christine 4 Veit, Alexander 4 Wachsmuth, Daniel 4 Wendland, Wolfgang L. 4 Wohlmuth, Barbara I. 4 Zhao, Shan 3 Alexov, Emil 3 Ali, Mazen 3 Banjai, Lehel 3 Bratsch, Michael 3 Bui-Thanh, Tan 3 Chinnamsetty, Sambasiva Rao 3 Chu, Moody T. 3 Coulier, Pieter 3 de Hoop, Maarten V. ...and 933 more Authors all top 5 Cited in 137 Serials 74 SIAM Journal on Scientific Computing 58 Computer Methods in Applied Mechanics and Engineering 56 Journal of Computational Physics 33 Numerische Mathematik 33 SIAM Journal on Matrix Analysis and Applications 27 Numerical Linear Algebra with Applications 25 Journal of Computational and Applied Mathematics 20 Computing 19 Computing and Visualization in Science 17 Journal of Scientific Computing 17 Linear Algebra and its Applications 16 Advances in Computational Mathematics 16 Computational Methods in Applied Mathematics 15 Mathematics of Computation 15 Engineering Analysis with Boundary Elements 14 SIAM/ASA Journal on Uncertainty Quantification 13 Applied Mathematics and Computation 13 Applied Numerical Mathematics 12 Computers & Mathematics with Applications 8 Constructive Approximation 8 Computational Mechanics 7 BIT 7 International Journal for Numerical Methods in Engineering 7 Multiscale Modeling & Simulation 6 SIAM Journal on Numerical Analysis 6 Numerical Algorithms 6 Computational Mathematics and Mathematical Physics 6 Foundations of Computational Mathematics 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Computer Physics Communications 4 Ukrainian Mathematical Journal 4 Applied Mathematics Letters 4 SIAM Review 4 Vietnam Journal of Mathematics 4 Acta Numerica 4 Communications in Computational Physics 3 Linear and Multilinear Algebra 3 Mathematics and Computers in Simulation 3 Numerical Functional Analysis and Optimization 3 SIAM Journal on Control and Optimization 3 Computer Aided Geometric Design 3 Journal of Integral Equations and Applications 3 Multidimensional Systems and Signal Processing 3 Computational Optimization and Applications 3 Applied and Computational Harmonic Analysis 3 Journal of Mathematical Sciences (New York) 3 ETNA. 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