Guo, Wei; Qiu, Jing-Mei A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps. (English) Zbl 07527716 J. Comput. Phys. 458, Article ID 111089, 24 p. (2022). MSC: 15Axx 65Mxx 65Fxx PDFBibTeX XMLCite \textit{W. Guo} and \textit{J.-M. Qiu}, J. Comput. Phys. 458, Article ID 111089, 24 p. (2022; Zbl 07527716) Full Text: DOI arXiv
Rörich, Anna; Werthmann, Tim A.; Göddeke, Dominik; Grasedyck, Lars Bayesian inversion for electromyography using low-rank tensor formats. (English) Zbl 1468.65179 Inverse Probl. 37, No. 5, Article ID 055003, 22 p. (2021). MSC: 65N21 65C05 65F50 62F15 78A46 78A70 78M31 92C55 35A01 35A02 15A72 PDFBibTeX XMLCite \textit{A. Rörich} et al., Inverse Probl. 37, No. 5, Article ID 055003, 22 p. (2021; Zbl 1468.65179) Full Text: DOI arXiv
Wu, Bijiao; Wang, Dingheng; Zhao, Guangshe; Deng, Lei; Li, Guoqi Hybrid tensor decomposition in neural network compression. (English) Zbl 1475.68325 Neural Netw. 132, 309-320 (2020). MSC: 68T07 15A23 15A69 PDFBibTeX XMLCite \textit{B. Wu} et al., Neural Netw. 132, 309--320 (2020; Zbl 1475.68325) Full Text: DOI arXiv
Bachmayr, Markus; Kazeev, Vladimir Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs. (English) Zbl 1454.65160 Found. Comput. Math. 20, No. 5, 1175-1236 (2020). MSC: 65N30 65N55 65N12 65F08 65F10 65F35 65Y20 15A69 35J25 PDFBibTeX XMLCite \textit{M. Bachmayr} and \textit{V. Kazeev}, Found. Comput. Math. 20, No. 5, 1175--1236 (2020; Zbl 1454.65160) Full Text: DOI arXiv
Zniyed, Yassine; Boyer, Rémy; de Almeida, André L. F.; Favier, Gérard A TT-based hierarchical framework for decomposing high-order tensors. (English) Zbl 1432.68621 SIAM J. Sci. Comput. 42, No. 2, A822-A848 (2020). MSC: 68W40 15A69 68T09 PDFBibTeX XMLCite \textit{Y. Zniyed} et al., SIAM J. Sci. Comput. 42, No. 2, A822--A848 (2020; Zbl 1432.68621) Full Text: DOI
Hackbusch, Wolfgang Tensor spaces and numerical tensor calculus. 2nd revised edition. (English) Zbl 07150978 Springer Series in Computational Mathematics 56. Cham: Springer (ISBN 978-3-030-35553-1/hbk; 978-3-030-35554-8/ebook). xxviii, 605 p. (2019). MSC: 65-02 15-02 PDFBibTeX XMLCite \textit{W. Hackbusch}, Tensor spaces and numerical tensor calculus. 2nd revised edition. Cham: Springer (2019; Zbl 07150978) Full Text: DOI
Fan, Hung-Yuan; Zhang, Liping; Chu, Eric King-wah; Wei, Yimin Numerical solution to a linear equation with tensor product structure. (English) Zbl 1438.65092 Numer. Linear Algebra Appl. 24, No. 6, e2106, 18 p. (2017). Reviewer: Fatemeh Panjeh Ali Beik (Rafsanjan) MSC: 65F99 15A06 15A69 65F10 65N22 PDFBibTeX XMLCite \textit{H.-Y. Fan} et al., Numer. Linear Algebra Appl. 24, No. 6, e2106, 18 p. (2017; Zbl 1438.65092) Full Text: DOI
Kressner, Daniel; Periša, Lana Recompression of Hadamard products of tensors in Tucker format. (English) Zbl 1373.65031 SIAM J. Sci. Comput. 39, No. 5, A1879-A1902 (2017). MSC: 65F30 15A69 65Y20 62-07 65F10 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{L. Periša}, SIAM J. Sci. Comput. 39, No. 5, A1879--A1902 (2017; Zbl 1373.65031) Full Text: DOI
Garreis, Sebastian; Ulbrich, Michael Constrained optimization with low-rank tensors and applications to parametric problems with PDEs. (English) Zbl 1381.49027 SIAM J. Sci. Comput. 39, No. 1, A25-A54 (2017). MSC: 49M15 65K05 90C15 65K15 15A69 PDFBibTeX XMLCite \textit{S. Garreis} and \textit{M. Ulbrich}, SIAM J. Sci. Comput. 39, No. 1, A25--A54 (2017; Zbl 1381.49027) Full Text: DOI
Beik, Fatemeh Panjeh Ali; Saberi Movahed, Farid; Ahmadi-Asl, Salman On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations. (English) Zbl 1413.65128 Numer. Linear Algebra Appl. 23, No. 3, 444-466 (2016). MSC: 65F30 15A24 15A69 PDFBibTeX XMLCite \textit{F. P. A. Beik} et al., Numer. Linear Algebra Appl. 23, No. 3, 444--466 (2016; Zbl 1413.65128) Full Text: DOI
Kressner, Daniel; Steinlechner, Michael; Vandereycken, Bart Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure. (English) Zbl 1382.65089 SIAM J. Sci. Comput. 38, No. 4, A2018-A2044 (2016). MSC: 65F10 65K05 15A69 58C05 65F08 PDFBibTeX XMLCite \textit{D. Kressner} et al., SIAM J. Sci. Comput. 38, No. 4, A2018--A2044 (2016; Zbl 1382.65089) Full Text: DOI
Fan, H.-Y.; Zhang, L.; Chu, E. K.-w.; Wei, Y. Q-less QR decomposition in inner product spaces. (English) Zbl 1391.65102 Linear Algebra Appl. 491, 292-316 (2016). MSC: 65F25 15A24 15A30 15A69 15A72 65F10 PDFBibTeX XMLCite \textit{H. Y. Fan} et al., Linear Algebra Appl. 491, 292--316 (2016; Zbl 1391.65102) Full Text: DOI
Da Silva, Curt; Herrmann, Felix J. Optimization on the hierarchical Tucker manifold - applications to tensor completion. (English) Zbl 1317.65136 Linear Algebra Appl. 481, 131-173 (2015). MSC: 65K05 90C48 15A69 53B21 65Y20 PDFBibTeX XMLCite \textit{C. Da Silva} and \textit{F. J. Herrmann}, Linear Algebra Appl. 481, 131--173 (2015; Zbl 1317.65136) Full Text: DOI arXiv
Kressner, Daniel; Tobler, Christine Algorithm 941: htucker – a Matlab toolbox for tensors in hierarchical Tucker format. (English) Zbl 1322.65054 ACM Trans. Math. Softw. 40, No. 3, Article No. 22, 22 p. (2014). MSC: 65F30 65Y15 15A69 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{C. Tobler}, ACM Trans. Math. Softw. 40, No. 3, Article No. 22, 22 p. (2014; Zbl 1322.65054) Full Text: DOI
Arnold, Andreas; Jahnke, Tobias On the approximation of high-dimensional differential equations in the hierarchical Tucker format. (English) Zbl 1308.65113 BIT 54, No. 2, 305-341 (2014). Reviewer: Yajuan Sun (Beijing) MSC: 65L05 65F99 15A69 PDFBibTeX XMLCite \textit{A. Arnold} and \textit{T. Jahnke}, BIT 54, No. 2, 305--341 (2014; Zbl 1308.65113) Full Text: DOI Link
Uschmajew, André; Vandereycken, Bart The geometry of algorithms using hierarchical tensors. (English) Zbl 1281.65062 Linear Algebra Appl. 439, No. 1, 133-166 (2013). MSC: 65F15 15A69 65F20 PDFBibTeX XMLCite \textit{A. Uschmajew} and \textit{B. Vandereycken}, Linear Algebra Appl. 439, No. 1, 133--166 (2013; Zbl 1281.65062) Full Text: DOI
Grasedyck, Lars; Kressner, Daniel; Tobler, Christine A literature survey of low-rank tensor approximation techniques. (English) Zbl 1279.65045 GAMM-Mitt. 36, No. 1, 53-78 (2013). MSC: 65F30 15A69 65F10 65F15 65-02 PDFBibTeX XMLCite \textit{L. Grasedyck} et al., GAMM-Mitt. 36, No. 1, 53--78 (2013; Zbl 1279.65045) Full Text: DOI arXiv
Lubich, Christian; Rohwedder, Thorsten; Schneider, Reinhold; Vandereycken, Bart Dynamical approximation by hierarchical Tucker and tensor-train tensors. (English) Zbl 1391.15087 SIAM J. Matrix Anal. Appl. 34, No. 2, 470-494 (2013). MSC: 15A69 90C06 65F99 65L05 PDFBibTeX XMLCite \textit{C. Lubich} et al., SIAM J. Matrix Anal. Appl. 34, No. 2, 470--494 (2013; Zbl 1391.15087) Full Text: DOI Link
Kressner, Daniel; Tobler, Christine Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems. (English) Zbl 1283.65025 Comput. Methods Appl. Math. 11, No. 3, 363-381 (2011). MSC: 65F15 15A18 15A69 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{C. Tobler}, Comput. Methods Appl. Math. 11, No. 3, 363--381 (2011; Zbl 1283.65025) Full Text: DOI Link
Kressner, Daniel; Tobler, Christine Low-rank tensor Krylov subspace methods for parametrized linear systems. (English) Zbl 1237.65034 SIAM J. Matrix Anal. Appl. 32, No. 4, 1288-1316 (2011). MSC: 65F10 15A69 65F08 35J25 65N30 60H15 35R60 60H35 65C30 PDFBibTeX XMLCite \textit{D. Kressner} and \textit{C. Tobler}, SIAM J. Matrix Anal. Appl. 32, No. 4, 1288--1316 (2011; Zbl 1237.65034) Full Text: DOI Link