Heidel, Gennadij; Khoromskaia, Venera; Khoromskij, Boris N.; Schulz, Volker Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints. (English) Zbl 07508470 J. Comput. Phys. 424, Article ID 109865, 21 p. (2021). MSC: 65-XX 15-XX PDFBibTeX XMLCite \textit{G. Heidel} et al., J. Comput. Phys. 424, Article ID 109865, 21 p. (2021; Zbl 07508470) Full Text: DOI arXiv
Khoromskaia, V.; Khoromskij, B. N. Prospects of tensor-based numerical modeling of the collective electrostatics in many-particle systems. (English) Zbl 1469.82010 Comput. Math. Math. Phys. 61, No. 5, 864-886 (2021). MSC: 82B20 82C22 82D60 81V70 81V55 15A69 78A30 78M16 82M22 PDFBibTeX XMLCite \textit{V. Khoromskaia} and \textit{B. N. Khoromskij}, Comput. Math. Math. Phys. 61, No. 5, 864--886 (2021; Zbl 1469.82010) Full Text: DOI arXiv
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N.; Yang, Chao Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation. (English) Zbl 1451.65054 J. Comput. Phys. 382, 221-239 (2019). MSC: 65F55 15A15 15A72 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Phys. 382, 221--239 (2019; Zbl 1451.65054) Full Text: DOI arXiv
Gavrilyuk, Ivan; Khoromskij, Boris N. Quasi-optimal rank-structured approximation to multidimensional parabolic problems by Cayley transform and Chebyshev interpolation. (English) Zbl 1420.65056 Comput. Methods Appl. Math. 19, No. 1, 55-71 (2019). MSC: 65F30 65F50 65N35 65F10 PDFBibTeX XMLCite \textit{I. Gavrilyuk} and \textit{B. N. Khoromskij}, Comput. Methods Appl. Math. 19, No. 1, 55--71 (2019; Zbl 1420.65056) Full Text: DOI
Gavrilyuk, Ivan (ed.); Khoromskij, Boris N. (ed.) Editorial. Tensor numerical methods: actual theory and recent applications. (English) Zbl 1422.00020 Comput. Methods Appl. Math. 19, No. 1, 1-4 (2019). MSC: 00B15 65-06 65F30 65F50 65N35 65F10 PDFBibTeX XMLCite \textit{I. Gavrilyuk} (ed.) and \textit{B. N. Khoromskij} (ed.), Comput. Methods Appl. Math. 19, No. 1, 1--4 (2019; Zbl 1422.00020) Full Text: DOI
Dolgov, Sergey V.; Kazeev, Vladimir A.; Khoromskij, Boris N. Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients. (English) Zbl 1484.65326 Math. Comput. Simul. 145, 136-155 (2018). MSC: 65N75 65N35 65F08 65F10 35J15 15A72 35R60 PDFBibTeX XMLCite \textit{S. V. Dolgov} et al., Math. Comput. Simul. 145, 136--155 (2018; Zbl 1484.65326) Full Text: DOI
Benner, Peter; Khoromskaia, Venera; Khoromskij, Boris N. Range-separated tensor format for many-particle modeling. (English) Zbl 1446.65202 SIAM J. Sci. Comput. 40, No. 2, A1034-A1062 (2018). MSC: 65P99 65F55 65F50 65N35 65F10 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM J. Sci. Comput. 40, No. 2, A1034--A1062 (2018; Zbl 1446.65202) Full Text: DOI arXiv
Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, Boris N.; Langer, Ulrich Low rank tensor methods in Galerkin-based isogeometric analysis. (English) Zbl 1439.65185 Comput. Methods Appl. Mech. Eng. 316, 1062-1085 (2017). MSC: 65N30 65D07 PDFBibTeX XMLCite \textit{A. Mantzaflaris} et al., Comput. Methods Appl. Mech. Eng. 316, 1062--1085 (2017; Zbl 1439.65185) Full Text: DOI HAL
Khoromskij, Boris; Repin, Sergey Rank structured approximation method for quasi-periodic elliptic problems. (English) Zbl 1380.65069 Comput. Methods Appl. Math. 17, No. 3, 457-477 (2017). MSC: 65F10 65F08 35J25 PDFBibTeX XMLCite \textit{B. Khoromskij} and \textit{S. Repin}, Comput. Methods Appl. Math. 17, No. 3, 457--477 (2017; Zbl 1380.65069) Full Text: DOI arXiv Link
Khoromskaia, Venera; Khoromskij, Boris N. Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach. (English) Zbl 1380.65355 Comput. Methods Appl. Math. 17, No. 3, 431-455 (2017). MSC: 65N25 35Q84 35P15 PDFBibTeX XMLCite \textit{V. Khoromskaia} and \textit{B. N. Khoromskij}, Comput. Methods Appl. Math. 17, No. 3, 431--455 (2017; Zbl 1380.65355) Full Text: DOI arXiv
Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N. Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation. (English) Zbl 1376.65045 J. Comput. Phys. 334, 221-239 (2017). MSC: 65F15 65F30 15A69 35Q35 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Phys. 334, 221--239 (2017; Zbl 1376.65045) Full Text: DOI arXiv
Khoromskaia, Venera; Khoromskij, Boris N. Fast tensor method for summation of long-range potentials on 3D lattices with defects. (English) Zbl 1413.65141 Numer. Linear Algebra Appl. 23, No. 2, 249-271 (2016). MSC: 65F30 15A69 65F15 82B20 PDFBibTeX XMLCite \textit{V. Khoromskaia} and \textit{B. N. Khoromskij}, Numer. Linear Algebra Appl. 23, No. 2, 249--271 (2016; Zbl 1413.65141) Full Text: DOI arXiv
Khoromskij, Boris N. Tensor numerical methods for multidimensional PDEs: theoretical analysis and initial applications. (English) Zbl 1382.65461 ESAIM, Proc. Surv. 48, 1-28 (2015). MSC: 65N99 65-02 PDFBibTeX XMLCite \textit{B. N. Khoromskij}, ESAIM, Proc. Surv. 48, 1--28 (2015; Zbl 1382.65461) Full Text: DOI arXiv
Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G. Polynomial chaos expansion of random coefficients and the solution of stochastic partial differential equations in the tensor train format. (English) Zbl 1329.65271 SIAM/ASA J. Uncertain. Quantif. 3, 1109-1135 (2015). MSC: 65N30 15A69 60H15 60H35 65N75 76M10 76S05 PDFBibTeX XMLCite \textit{S. Dolgov} et al., SIAM/ASA J. Uncertain. Quantif. 3, 1109--1135 (2015; Zbl 1329.65271) Full Text: DOI arXiv
Dolgov, Sergey; Khoromskij, Boris Simultaneous state-time approximation of the chemical master equation using tensor product formats. (English) Zbl 1363.65117 Numer. Linear Algebra Appl. 22, No. 2, 197-219 (2015). MSC: 65L05 15A69 92E20 34A34 65Y20 PDFBibTeX XMLCite \textit{S. Dolgov} and \textit{B. Khoromskij}, Numer. Linear Algebra Appl. 22, No. 2, 197--219 (2015; Zbl 1363.65117) Full Text: DOI arXiv
Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, B. N.; Langer, Ulrich Matrix generation in isogeometric analysis by low rank tensor approximation. (English) Zbl 1360.65282 Boissonnat, Jean-Daniel (ed.) et al., Curves and surfaces. 8th international conference, Paris, France, June 12–18, 2014. Revised selected papers. Cham: Springer (ISBN 978-3-319-22803-7/pbk; 978-3-319-22804-4/ebook). Lecture Notes in Computer Science 9213, 321-340 (2015). MSC: 65N30 35J25 PDFBibTeX XMLCite \textit{A. Mantzaflaris} et al., Lect. Notes Comput. Sci. 9213, 321--340 (2015; Zbl 1360.65282) Full Text: DOI HAL
Khoromskaia, Venera; Khoromskij, Boris N. Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation. (English) Zbl 1360.78016 Comput. Phys. Commun. 185, No. 12, 3162-3174 (2014). MSC: 78A30 PDFBibTeX XMLCite \textit{V. Khoromskaia} and \textit{B. N. Khoromskij}, Comput. Phys. Commun. 185, No. 12, 3162--3174 (2014; Zbl 1360.78016) Full Text: DOI arXiv
Dolgov, S. V.; Khoromskij, B. N.; Oseledets, I. V.; Savostyanov, D. V. Computation of extreme eigenvalues in higher dimensions using block tensor train format. (English) Zbl 1344.65043 Comput. Phys. Commun. 185, No. 4, 1207-1216 (2014). MSC: 65F15 65Y20 PDFBibTeX XMLCite \textit{S. V. Dolgov} et al., Comput. Phys. Commun. 185, No. 4, 1207--1216 (2014; Zbl 1344.65043) Full Text: DOI arXiv Link
Khoromskaia, V.; Khoromskij, B. N. Møller-Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals. (English) Zbl 1344.65035 Comput. Phys. Commun. 185, No. 1, 2-10 (2014). MSC: 65D30 81V70 81V55 PDFBibTeX XMLCite \textit{V. Khoromskaia} and \textit{B. N. Khoromskij}, Comput. Phys. Commun. 185, No. 1, 2--10 (2014; Zbl 1344.65035) Full Text: DOI
Bertoglio, Cristóbal; Khoromskij, Boris N. Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels. (English) Zbl 1308.65213 Comput. Phys. Commun. 183, No. 4, 904-912 (2012). MSC: 65R10 65D30 PDFBibTeX XMLCite \textit{C. Bertoglio} and \textit{B. N. Khoromskij}, Comput. Phys. Commun. 183, No. 4, 904--912 (2012; Zbl 1308.65213) Full Text: DOI
Hackbusch, Wolfgang; Khoromskij, Boris N.; Sauter, Stefan; Tyrtyshnikov, Eugene E. Use of tensor formats in elliptic eigenvalue problems. (English) Zbl 1274.35252 Numer. Linear Algebra Appl. 19, No. 1, 133-151 (2012). Reviewer: Ivan V. Oseledets (Moskva) MSC: 35P05 15A69 PDFBibTeX XMLCite \textit{W. Hackbusch} et al., Numer. Linear Algebra Appl. 19, No. 1, 133--151 (2012; Zbl 1274.35252) Full Text: DOI
Dolgov, Sergey; Khoromskij, Boris; Savostyanov, Dmitry Superfast Fourier transform using QTT approximation. (English) Zbl 1260.65114 J. Fourier Anal. Appl. 18, No. 5, 915-953 (2012). Reviewer: S. F. Lukomskii (Saratov) MSC: 65T50 15A69 65Y20 PDFBibTeX XMLCite \textit{S. Dolgov} et al., J. Fourier Anal. Appl. 18, No. 5, 915--953 (2012; Zbl 1260.65114) Full Text: DOI
Khoromskij, Boris N. \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling. (English) Zbl 1228.65069 Constr. Approx. 34, No. 2, 257-280 (2011). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 65F50 15A69 PDFBibTeX XMLCite \textit{B. N. Khoromskij}, Constr. Approx. 34, No. 2, 257--280 (2011; Zbl 1228.65069) Full Text: DOI
Fedorov, M. V.; Flad, H.-J.; Chuev, G. N.; Grasedyck, L.; Khoromskij, B. N. A structured low-rank wavelet solver for the Ornstein-Zernike integral equation. (English) Zbl 1117.65170 Computing 80, No. 1, 47-73 (2007). MSC: 65R20 45E10 65T60 PDFBibTeX XMLCite \textit{M. V. Fedorov} et al., Computing 80, No. 1, 47--73 (2007; Zbl 1117.65170) Full Text: DOI
Hackbusch, W.; Khoromskij, B. N. Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators. (English) Zbl 1087.65050 Computing 76, No. 3-4, 203-225 (2006). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65J05 65F50 65F30 46B28 47A80 65R20 45P05 65N38 PDFBibTeX XMLCite \textit{W. Hackbusch} and \textit{B. N. Khoromskij}, Computing 76, No. 3--4, 203--225 (2006; Zbl 1087.65050) Full Text: DOI
Gavrilyuk, Ivan P.; Hackbusch, Wolfgang; Khoromskij, Boris N. Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. (English) Zbl 1071.65032 Computing 74, No. 2, 131-157 (2005). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65F05 65F50 65F30 46B28 47A80 PDFBibTeX XMLCite \textit{I. P. Gavrilyuk} et al., Computing 74, No. 2, 131--157 (2005; Zbl 1071.65032) Full Text: DOI