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The consistent use of tensor formats can be regarded as a base for a new class of rank\u2010truncated iterative eigensolvers. The computational cost is almost linear in the univariate problem size <jats:italic>n<\/jats:italic>, while traditional method scale like <jats:italic>n<\/jats:italic><jats:sup><jats:italic>d<\/jats:italic><\/jats:sup>. Tensor methods can be applied to solving large\u2010scale spectral problems in computational quantum chemistry, for example, the Schr\u00f6dinger, Hartree\u2013Fock and Kohn\u2013Sham equations in electronic structure calculations. The results of numerical experiments clearly indicate the linear\u2010logarithmic scaling of the low\u2010rank tensor method in <jats:italic>n<\/jats:italic>. The algorithms work equally well for the computation of both minimal and maximal eigenvalues of the discrete elliptic operators. Copyright \u00a9\u20092011 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.793","type":"journal-article","created":{"date-parts":[[2011,10,18]],"date-time":"2011-10-18T08:03:52Z","timestamp":1318925032000},"page":"133-151","source":"Crossref","is-referenced-by-count":24,"title":["Use of tensor formats in elliptic eigenvalue problems"],"prefix":"10.1002","volume":"19","author":[{"given":"Wolfgang","family":"Hackbusch","sequence":"first","affiliation":[{"name":"Max\u2010Planck\u2010Institut f\u00fcr Mathematik in den Naturwissenschaften  Inselstr. 22\u201026 D\u201004103, Leipzig Germany"}]},{"given":"Boris N.","family":"Khoromskij","sequence":"additional","affiliation":[{"name":"Max\u2010Planck\u2010Institut f\u00fcr Mathematik in den Naturwissenschaften  Inselstr. 22\u201026 D\u201004103, Leipzig Germany"}]},{"given":"Stefan","family":"Sauter","sequence":"additional","affiliation":[{"name":"Universit\u00e4tZ\u00fcrich  Switzerland"}]},{"given":"Eugene\u2009E.","family":"Tyrtyshnikov","sequence":"additional","affiliation":[{"name":"Institute of Numerical Mathematics Russian Academy of Sciences  Gubkina 8, 119333 Moscow Russia"}]}],"member":"311","published-online":{"date-parts":[[2011,10,18]]},"reference":[{"key":"e_1_2_9_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-8659(05)80042-0"},{"key":"e_1_2_9_1_3_1","volume-title":"Le\u00e7ons sur les Propri\u00e9t\u00e9s Extr\u00e9males et la Meilleure Approximation des Fonctions Analytiques D'une Variable R\u00e9elle","author":"Bernstein SN","year":"1926"},{"key":"e_1_2_9_1_4_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.112329799"},{"key":"e_1_2_9_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/040604959"},{"key":"e_1_2_9_1_6_1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/dri015"},{"key":"e_1_2_9_1_7_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.2761871"},{"key":"e_1_2_9_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898346995"},{"key":"e_1_2_9_1_9_1","unstructured":"EspigM.Approximation mit Elementartensorsummen Doctoral thesis Universit\u00e4t Leipzig 2008."},{"key":"e_1_2_9_1_10_1","first-page":"1","article-title":"Verification of the cross 3d algorithm on quantum chemistry data","volume":"4","author":"Flad H\u2010J","year":"2008","journal-title":"Rus. 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