{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T11:55:08Z","timestamp":1773662108695,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In the recent years, multidimensional numerical simulations with tensor-structured data formats have been\nrecognized  as the basic concept for breaking  the \"curse of dimensionality\".\nModern applications of tensor methods include the challenging high-dimensional\nproblems of material sciences, bio-science, stochastic modeling, signal processing,\nmachine learning, and data mining, financial mathematics, etc.\n   The guiding principle of the tensor methods\nis an approximation of multivariate functions and operators\nwith some separation of variables to keep the computational process in\na low parametric tensor-structured manifold.\n   Tensors structures had been wildly used as models of data and\ndiscussed in the contexts of differential geometry, mechanics,\nalgebraic geometry, data analysis etc. before tensor methods recently\nhave penetrated into numerical computations.  On the one hand, the existing tensor\nrepresentation formats remained to be of a limited use in many high-dimensional problems\nbecause of lack of sufficiently reliable and fast software.\nOn the other hand, for moderate dimensional problems (e.g. in\n\"ab-initio\" quantum chemistry) as well as for selected model problems\nof very high dimensions,  the application of traditional canonical\nand Tucker formats in combination with the ideas of multilevel methods\nhas led to the new efficient algorithms.\n   The recent progress in tensor numerical methods is achieved with new\nrepresentation formats now known as  \"tensor-train representations\"\nand \"hierarchical Tucker representations\". Note that the formats themselves could have\nbeen picked up earlier in the literature on the modeling of quantum systems.\nUntil 2009 they lived in a closed world of those\nquantum theory publications and never trespassed the territory of\nnumerical analysis. The tremendous progress\nduring the very recent years shows  the new tensor tools in various\napplications and in the development of these tools and study of\ntheir approximation and algebraic properties.\n  This special issue treats tensors as a base for efficient\nnumerical algorithms  in various modern applications and with  special\nemphases on the new representation formats.<\/jats:p>","DOI":"10.2478\/cmam-2011-0014","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T11:29:25Z","timestamp":1366025365000},"page":"272-272","source":"Crossref","is-referenced-by-count":0,"title":["Preface to the special issue, CMAM 2011, no. 3."],"prefix":"10.2478","volume":"11","author":[{"given":"Ivan","family":"Gavrilyuk","sequence":"first","affiliation":[{"name":"Staatliche Studienakademie Th\u00fcringen, Berufsakademie Eisenach, University of Cooperative Education, Am Wartenberg 2, D-99817 Eisenach, Germany."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boris","family":"Khoromskij","sequence":"additional","affiliation":[{"name":"Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eugene","family":"Tyrtyshnikov","sequence":"additional","affiliation":[{"name":"Institute of Numerical Mathematics, Russian Academy of Sciences, 8 Gubkin Street, Moscow, 119333, Russia."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2011]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/11\/3\/article-p272.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.2478\/cmam-2011-0014\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.2478\/cmam-2011-0014\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:58:08Z","timestamp":1773658688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.2478\/cmam-2011-0014\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2011]]},"published-print":{"date-parts":[[2011]]}},"alternative-id":["10.2478\/cmam-2011-0014"],"URL":"https:\/\/doi.org\/10.2478\/cmam-2011-0014","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2011]]}}}