{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T16:04:00Z","timestamp":1785254640402,"version":"3.55.0"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,11,14]],"date-time":"2016-11-14T00:00:00Z","timestamp":1479081600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["FP7 Advanced Grant AdG247277"],"award-info":[{"award-number":["FP7 Advanced Grant AdG247277"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["14-11-00659"],"award-info":[{"award-number":["14-11-00659"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2017,4]]},"DOI":"10.1007\/s10444-016-9491-y","type":"journal-article","created":{"date-parts":[[2016,11,14]],"date-time":"2016-11-14T05:43:06Z","timestamp":1479102186000},"page":"411-442","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["QTT-finite-element approximation for multiscale problems I: model problems in one dimension"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9445-3267","authenticated-orcid":false,"given":"Vladimir","family":"Kazeev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivan","family":"Oseledets","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxim","family":"Rakhuba","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Schwab","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,11,14]]},"reference":[{"issue":"2","key":"9491_CR1","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1002\/nla.1951","volume":"22","author":"R Andreev","year":"2015","unstructured":"Andreev, R., Tobler, C.: Multilevel preconditioning and low-rank tensor iteration for spacetime simultaneous discretizations of parabolic pdes. Numer. Linear Algebra Appl. 22(2), 317\u2013337 (2015). doi: 10.1002\/nla.1951","journal-title":"Numer. Linear Algebra Appl."},{"issue":"4","key":"9491_CR2","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1007\/BF02165003","volume":"16","author":"I Babu\u0161ka","year":"1971","unstructured":"Babu\u0161ka, I.: Error-bounds for finite element method. Numer. Math. 16(4), 322\u2013333 (1971). doi: 10.1007\/BF02165003","journal-title":"Numer. Math."},{"key":"9491_CR3","unstructured":"Bachmayr, M., Dahmen, W.: Adaptive low-rank methods for problems on Sobolev spaces with error control in L 2. arXiv: 1412.3951 . (2014)"},{"key":"9491_CR4","doi-asserted-by":"publisher","unstructured":"Bakhvalov, N., Panasenko, G.: Homogenisation: Averaging processes in periodic media, Mathematics and its Applications, vol. 36. Springer. doi: 10.1007\/978-94-009-2247-1","DOI":"10.1007\/978-94-009-2247-1"},{"key":"9491_CR5","doi-asserted-by":"publisher","unstructured":"Ballani, J., Grasedyck, L.: A projection method to solve linear systems in tensor format. doi: 10.1002\/nla.1818 (2012)","DOI":"10.1002\/nla.1818"},{"key":"9491_CR6","doi-asserted-by":"publisher","unstructured":"Buffa, A., Sangalli, G., Schwab, C.: Exponential convergence of the hp version of isogeometric analysis in 1D. In: Proceedings. doi: 10.1007\/978-3-319-01601-6_15 (2014)","DOI":"10.1007\/978-3-319-01601-6_15"},{"key":"9491_CR7","unstructured":"Davis, P.J.: Interpolation and approximation. Dover Publications (1975)"},{"issue":"6","key":"9491_CR8","doi-asserted-by":"publisher","first-page":"A3016","DOI":"10.1137\/120864210","volume":"34","author":"S Dolgov","year":"2012","unstructured":"Dolgov, S., Khoromskij, B., Oseledets, I.: Fast solution of parabolic problems in the tensor train\/quantized tensor train format with initial application to the fokker\u2013planck equation. SIAM J. Sci. Comput. 34(6), A3016\u2013A3038 (2012). doi: 10.1137\/120864210","journal-title":"SIAM J. Sci. Comput."},{"key":"9491_CR9","unstructured":"Dolgov, S.V., Kazeev, V.A., Khoromskij, B.N.: The tensor-structured solution of one-dimensional elliptic differential equations with high-dimensional parameters. Preprint 51, Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften. http:\/\/www.mis.mpg.de\/publications\/preprints\/2012\/prepr2012-51.html (2012)"},{"key":"9491_CR10","unstructured":"Dolgov, S.V., Khoromskij, B.N.: Tensor-product approach to global time-space-parametric discretization of chemical master equation. Preprint 68, Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften. http:\/\/www.mis.mpg.de\/publications\/preprints\/2012\/prepr2012-68.html (2012)"},{"key":"9491_CR11","unstructured":"Dolgov, S.V., Khoromskij, B.N., Oseledets, I.V., Tyrtyshnikov, E.E.: Tensor structured iterative solution of elliptic problems with jumping coefficients. Preprint 55, Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften. http:\/\/www.mis.mpg.de\/publications\/preprints\/2010\/prepr2010-55.html (2010)"},{"issue":"5","key":"9491_CR12","doi-asserted-by":"publisher","first-page":"A2248","DOI":"10.1137\/140953289","volume":"36","author":"SV Dolgov","year":"2014","unstructured":"Dolgov, S.V., Savostyanov, D.V.: Alternating minimal energy methods for linear systems in higher dimensions. SIAM J. Sci. Comput. 36(5), A2248\u2013A2271 (2014). doi: 10.1137\/140953289","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"9491_CR13","doi-asserted-by":"publisher","first-page":"2029","DOI":"10.1137\/090764189","volume":"31","author":"L Grasedyck","year":"2010","unstructured":"Grasedyck, L.: Hierarchical singular value decomposition of tensors. SIAM Journal on Matrix Analysis and Applications 31(4), 2029\u20132054 (2010). doi: 10.1137\/090764189 . http:\/\/link.aip.org\/link\/?SML\/31\/2029\/1","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"9491_CR14","unstructured":"Grasedyck, L.: Polynomial approximation in hierarchical Tucker format by vector-tensorization. Preprint 308, Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen. http:\/\/www.igpm.rwth-aachen.de\/Download\/reports\/pdf\/IGPM308_k.pdf (2010)"},{"issue":"1","key":"9491_CR15","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1002\/gamm.201310004","volume":"36","author":"L Grasedyck","year":"2013","unstructured":"Grasedyck, L., Kressner, D., Tobler, C.: A literature survey of low-rank tensor approximation techniques. GAMM-Mitteilungen 36(1), 53\u201378 (2013). doi: 10.1002\/gamm.201310004","journal-title":"GAMM-Mitteilungen"},{"key":"9491_CR16","doi-asserted-by":"publisher","unstructured":"Hackbusch, W.: Tensor Spaces and Numerical Tensor Calculus, Springer Series in Computational Mathematics, vol. 42. Springer (2012). doi: 10.1007\/978-3-642-28027-6 . http:\/\/www.springerlink.com\/content\/l62t86","DOI":"10.1007\/978-3-642-28027-6"},{"issue":"5","key":"9491_CR17","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1007\/s00041-009-9094-9","volume":"15","author":"W Hackbusch","year":"2009","unstructured":"Hackbusch, W., K\u00fchn, S.: A new scheme for the tensor representation. J. Fourier Anal. Appl. 15(5), 706\u2013722 (2009). doi: http:\/\/www.springerlink.com\/content\/t3747nk47m368g44 , 10.1007\/s00041-009-9094-9","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"9491_CR18","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1137\/030601077","volume":"3","author":"VH Hoang","year":"2005","unstructured":"Hoang, V.H., Schwab, C.: High-dimensional finite elements for elliptic problems with multiple scales. Multiscale Model. Simul. 3(1), 168\u2013194 (2005). doi: 10.1137\/030601077","journal-title":"Multiscale Model. Simul."},{"issue":"2","key":"9491_CR19","doi-asserted-by":"publisher","first-page":"A683","DOI":"10.1137\/100818893","volume":"34","author":"S Holtz","year":"2012","unstructured":"Holtz, S., Rohwedder, T., Schneider, R.: The alternating linear scheme for tensor optimization in the Tensor Train format. SIAM J. Sci. Comput. 34(2), A683\u2013A713 (2012). doi: 10.1137\/100818893","journal-title":"SIAM J. Sci. Comput."},{"key":"9491_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/b98828","volume-title":"Finite element analysis of acoustic scattering, Applied Mathematical Sciences, vol. 132","author":"F Ihlenburg","year":"1998","unstructured":"Ihlenburg, F.: Finite element analysis of acoustic scattering, Applied Mathematical Sciences, vol. 132. Springer, New York (1998). doi: 10.1007\/b98828"},{"key":"9491_CR21","unstructured":"Jikov, V.V., Kozlov, S.M., Oleinik, O.A.: Homogenization of Differential Operators and Integral Functionals. Springer (1994). http:\/\/www.springer.com\/book\/9783642846618"},{"issue":"1-2","key":"9491_CR22","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/BF01896769","volume":"27","author":"HT Kau","year":"1976","unstructured":"Kau, H.T.: An inequality for algebraic polynomials, and the dependence between the best polynomial approximations e ( f ) L p $e(f)_{L_{p}}$ and e ( f ) L q $e(f)_{L_{q}}$ of functions f(x)L p (in Russian). Acta Math. Acad. Sci. Hung. 27 (1-2), 141\u2013147 (1976). doi: 10.1007\/BF01896769","journal-title":"Acta Math. Acad. Sci. Hung."},{"key":"9491_CR23","doi-asserted-by":"publisher","unstructured":"Kazeev, V.: Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Ph.D. thesis, SAM, ETH Zurich, ETH Dissertation No. 23002. doi: 10.3929\/ethz-a-010554062 . http:\/\/e-collection.library.ethz.ch\/view\/eth:48314","DOI":"10.3929\/ethz-a-010554062"},{"key":"9491_CR24","unstructured":"Kazeev, V.: Tensor-structured multilevel approximation of polynomial and piecewise-analytic functions (in preparation)"},{"key":"9491_CR25","doi-asserted-by":"publisher","unstructured":"Kazeev, V., Khammash, M., Nip, M., Schwab, C.: Direct solution of the chemical master equation using quantized tensor trains. PLoS Comput. Biol. 10 (3) (2014). doi: 10.1371\/journal.pcbi.1003359","DOI":"10.1371\/journal.pcbi.1003359"},{"key":"9491_CR26","unstructured":"Kazeev, V., Reichmann, O., Schwab, C.: hp-DG-QTT solution of high-dimensional degenerate diffusion equations. Research Report 11, Seminar for Applied Mathematics, ETH Z\u00fcrich. http:\/\/www.sam.math.ethz.ch\/reports\/2012\/11 (2012)"},{"key":"9491_CR27","doi-asserted-by":"publisher","unstructured":"Kazeev, V., Reichmann, O., Schwab, C.: Low-rank tensor structure of linear diffusion operators in the TT and QTT formats. Linear Algebra Appl. (2013). doi: 10.1016\/j.laa.2013.01.009","DOI":"10.1016\/j.laa.2013.01.009"},{"key":"9491_CR28","doi-asserted-by":"publisher","unstructured":"Kazeev, V., Schwab, C.: Approximation of singularities by quantized-tensor FEM. In: Proceedings in Applied Mathematics and Mechanics. doi: 10.1002\/pamm.201510353 , vol. 15, pp 743\u2013746 (2015)","DOI":"10.1002\/pamm.201510353"},{"key":"9491_CR29","unstructured":"Kazeev, V., Schwab, C.: Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Research Report 24, Seminar for Applied Mathematics, ETH Z\u00fcrich. http:\/\/www.sam.math.ethz.ch\/reports\/2015\/24 (2015)"},{"issue":"3","key":"9491_CR30","doi-asserted-by":"publisher","first-page":"1221","DOI":"10.1137\/130927218","volume":"36","author":"V Kazeev","year":"2015","unstructured":"Kazeev, V., Schwab, C.: Tensor approximation of stationary distributions of chemical reaction networks. SIAM J. Matrix Anal. Appl. 36(3), 1221\u20131247 (2015). doi: 10.1137\/130927218","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"9491_CR31","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1137\/100820479","volume":"33","author":"VA Kazeev","year":"2012","unstructured":"Kazeev, V.A., Khoromskij, B.N.: Low-rank explicit QTT representation of the Laplace operator and its inverse. SIAM J. Matrix Anal. Appl. 33(3), 742\u2013758 (2012). doi: 10.1137\/100820479","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9491_CR32","doi-asserted-by":"crossref","unstructured":"Kazeev, V.A., Khoromskij, B.N., Tyrtyshnikov, E.E.: Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity. SIAM J. Sci. Comput. (2013)","DOI":"10.1137\/110844830"},{"issue":"2","key":"9491_CR33","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s00365-011-9131-1","volume":"34","author":"BN Khoromskij","year":"2011","unstructured":"Khoromskij, B.N.: \ud835\udcde ( d n ) $\\mathcal {O}(d n)$ -quantics approximation of n-d tensors in high-dimensional numerical modeling. Constr. Approx. 34(2), 257\u2013280 (2011). doi: 10.1007\/s00365-011-9131-1","journal-title":"Constr. Approx."},{"issue":"1","key":"9491_CR34","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1137\/090777372","volume":"33","author":"BN Khoromskij","year":"2011","unstructured":"Khoromskij, B.N., Khoromskaia, V., Flad, H.J.: Numerical solution of the Hartre-Fock equation in multilevel tensor-structured format. SIAM J. Sci. Comput. 33(1), 45\u201365 (2011). doi: 10.1137\/090777372 . http:\/\/link.aip.org\/link\/?SCE\/33\/45\/1","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"9491_CR35","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1515\/rnam-2015-0030","volume":"30","author":"BN Khoromskij","year":"2015","unstructured":"Khoromskij, B.N., Oseledets, I.V.: A fast iteration method for solving elliptic problems with quasiperiodic coefficients. Russ. J. Numer. Anal. Math. Model. 30(6), 329\u2013344 (2015). doi: 10.1515\/rnam-2015-0030 . http:\/\/www.degruyter.com\/view\/j\/rnam.2015.30.issue-6\/rnam-2015-0030\/rnam-2015-0030.xml","journal-title":"Russ. J. Numer. Anal. Math. Model."},{"issue":"1","key":"9491_CR36","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1137\/100785715","volume":"33","author":"BN Khoromskij","year":"2011","unstructured":"Khoromskij, B.N., Schwab, C.: Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. SIAM J. Sci. Comput. 33(1), 364\u2013385 (2011). http:\/\/epubs.siam.org\/sisc\/resource\/1\/sjoce3\/v33\/i1\/p364_s1","journal-title":"SIAM J. Sci. Comput."},{"key":"9491_CR37","unstructured":"Kressner, D., Steinlechner, M., Uschmajew, A.: Low-rank tensor methods with subspace correction for symmetric eigenvalue problems. Technical report 40, MATHICSE EPFL. http:\/\/sma.epfl.ch\/~anchpcommon\/publications\/EVAMEN.pdf (2013)"},{"key":"9491_CR38","unstructured":"Kressner, D., Steinlechner, M., Vandereycken, B.: A fast iteration method for solving elliptic problems with quasiperiodic coefficients. arXiv: 1508.02988 (2015)"},{"key":"9491_CR39","unstructured":"Maday, Y., Mula, O., Turinici, G.: Convergence analysis of the generalized empirical interpolation method. Tech. rep., HAL-UPMC. http:\/\/hal.upmc.fr\/file\/index\/docid\/1032458\/filename\/maday_mula_turinici_ConvRates_SINUM_Submitted.pdf"},{"key":"9491_CR40","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1017\/S1446788700038878","volume":"25","author":"RJ Nessel","year":"1978","unstructured":"Nessel, R.J., Wilmes, G.: Nikolskii-type inequalities for trigonometric polynomials and entire functions of exponential type. J. Aust. Math. Soc. Ser. A 25, 7\u201318 (1978). doi: 10.1017\/S1446788700038878","journal-title":"J. Aust. Math. Soc. Ser. A"},{"key":"9491_CR41","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1134\/S1064562409050056","volume":"80","author":"I Oseledets","year":"2009","unstructured":"Oseledets, I.: Approximation of matrices with logarithmic number of parameters. Dokl. Math. 80, 653\u2013654 (2009). doi: 10.1134\/S1064562409050056","journal-title":"Dokl. Math."},{"issue":"5","key":"9491_CR42","doi-asserted-by":"publisher","first-page":"A2718","DOI":"10.1137\/110833142","volume":"34","author":"I Oseledets","year":"2012","unstructured":"Oseledets, I., Dolgov, S.: Solution of linear systems and matrix inversion in the TT-format. SIAM J. Sci. Comput. 34(5), A2718\u2013A2739 (2012). doi: 10.1137\/110833142","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"9491_CR43","doi-asserted-by":"publisher","first-page":"2130","DOI":"10.1137\/090757861","volume":"31","author":"IV Oseledets","year":"2010","unstructured":"Oseledets, I.V.: Approximation of 2 d 2 d matrices using tensor decomposition. SIAM J. Matrix Anal. Appl. 31(4), 2130\u20132145 (2010). doi: 10.1137\/090757861 . http:\/\/link.aip.org\/link\/?SML\/31\/2130\/1","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"5","key":"9491_CR44","doi-asserted-by":"publisher","first-page":"2295","DOI":"10.1137\/090752286","volume":"33","author":"IV Oseledets","year":"2011","unstructured":"Oseledets, I.V.: Tensor train decomposition. SIAM J. Sci. Comput. 33(5), 2295\u20132317 (2011). doi: 10.1137\/090752286","journal-title":"SIAM J. Sci. Comput."},{"key":"9491_CR45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00365-012-9175-x","volume":"37","author":"IV Oseledets","year":"2013","unstructured":"Oseledets, I.V.: Constructive representation of functions in tensor formats. Constr. Approx. 37, 1\u201318 (2013). http:\/\/link.springer.com\/article\/10.1007\/s00365-012-9175-x","journal-title":"Constr. Approx."},{"issue":"5","key":"9491_CR46","doi-asserted-by":"publisher","first-page":"3744","DOI":"10.1137\/090748330","volume":"31","author":"IV Oseledets","year":"2009","unstructured":"Oseledets, I.V., Tyrtyshnikov, E.E.: Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput. 31(5), 3744\u20133759 (2009). doi: 10.1137\/090748330 . http:\/\/epubs.siam.org\/sisc\/resource\/1\/sjoce3\/v31\/i5\/p3744_s1","journal-title":"SIAM J. Sci. Comput."},{"key":"9491_CR47","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69894-1","volume-title":"n-widths in approximation theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 7","author":"A Pinkus","year":"1985","unstructured":"Pinkus, A.: n-widths in approximation theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 7. Springer, Berlin (1985). doi: 10.1007\/978-3-642-69894-1"},{"key":"9491_CR48","unstructured":"Quarteroni, A., Manzoni, A., Negri, F.: Reduced Basis Methods for Partial Differential Equations, UNITEXT, vol. 92. Springer (2016). http:\/\/link.springer.com\/book\/10.1007\/978-3-319-15431-2"},{"key":"9491_CR49","volume-title":"P- and H p-FEM: Theory and Application to Solid and Fluid Mechanics","author":"C Schwab","year":"1998","unstructured":"Schwab, C.: P- and H p-FEM: Theory and Application to Solid and Fluid Mechanics. Oxford University Press, Oxford (1998)"},{"issue":"5","key":"9491_CR50","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1070\/SM2003v194n06ABEH000747","volume":"194","author":"EE Tyrtyshnikov","year":"2003","unstructured":"Tyrtyshnikov, E.E.: Tensor approximations of matrices generated by asymptotically smooth functions. Sbornik: Math. 194 (5), 941\u2013954 (2003). doi: 10.1070\/SM2003v194n06ABEH000747 . http:\/\/iopscience.iop.org\/1064-5616\/194\/6\/A09","journal-title":"Sbornik: Math."},{"issue":"2","key":"9491_CR51","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s00211-010-0338-z","volume":"118","author":"L Beir\u00e3o da Veiga","year":"2011","unstructured":"Beir\u00e3o da Veiga, L., Buffa, A., Rivas, J., Sangalli, G.: Some estimates for hpk-refinement in isogeometric analysis. Numer. Math. 118(2), 271\u2013305 (2011). doi: 10.1007\/s00211-010-0338-z","journal-title":"Numer. Math."},{"issue":"22","key":"9491_CR52","doi-asserted-by":"publisher","first-page":"227,205","DOI":"10.1103\/PhysRevLett.93.227205","volume":"93","author":"F Verstraete","year":"2004","unstructured":"Verstraete, F., Porras, D., Cirac, J.I.: Density matrix renormalization group and periodic boundary conditions: A quantum information perspective. Phys. Rev. Lett. 93(22), 227,205 (2004). doi: 10.1103\/PhysRevLett.93.227205","journal-title":"Phys. Rev. Lett."},{"issue":"14","key":"9491_CR53","doi-asserted-by":"publisher","first-page":"147,902","DOI":"10.1103\/PhysRevLett.91.147902","volume":"91","author":"G Vidal","year":"2003","unstructured":"Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91(14), 147,902 (2003). doi: 10.1103\/PhysRevLett.91.147902","journal-title":"Phys. Rev. Lett."},{"issue":"14","key":"9491_CR54","doi-asserted-by":"publisher","first-page":"10,345","DOI":"10.1103\/PhysRevB.48.10345","volume":"48","author":"SR White","year":"1993","unstructured":"White, S.R.: Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48(14), 10,345\u201310,356 (1993). doi: 10.1103\/PhysRevB.48.10345","journal-title":"Phys. Rev. B"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9491-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-016-9491-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9491-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T23:31:00Z","timestamp":1498347060000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-016-9491-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,14]]},"references-count":54,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["9491"],"URL":"https:\/\/doi.org\/10.1007\/s10444-016-9491-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,14]]}}}