{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:36Z","timestamp":1787337216226,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"ERC-STG-2014","award":["639508"],"award-info":[{"award-number":["639508"]}]},{"name":"Research Council Norway","award":["179568\/V30"],"award-info":[{"award-number":["179568\/V30"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schr\u00f6dinger equation is here developed. We prove an existence and uniqueness result, both in the full infinite-dimensional amplitude space as well as for discretized versions of it. The extended coupled-cluster method is formulated as a critical point of an energy function using a generalization of the Rayleigh--Ritz principle: the bivariational principle. This gives a quadratic bound for the energy error in the discretized case. The existence and uniqueness results are proved using a type of monotonicity property for the flipped gradient of the energy function. A comparison to the analysis of the standard coupled-cluster method is made, and it is argued that the bivariational principle is a useful tool, both for studying coupled-cluster type methods and for developing new computational schemes in general.<\/jats:p>","DOI":"10.1137\/17m1116611","type":"journal-article","created":{"date-parts":[[2018,3,15]],"date-time":"2018-03-15T15:52:56Z","timestamp":1521129176000},"page":"660-683","source":"Crossref","is-referenced-by-count":18,"title":["Analysis of the Extended Coupled-Cluster Method in Quantum Chemistry"],"prefix":"10.1137","volume":"56","author":[{"given":"Andre","family":"Laestadius","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simen","family":"Kvaal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,3,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(83)90284-1"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01119617"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1063\/1.1727484"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01119616"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0029-5582(58)90280-3"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/0029-5582(60)90140-1"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevC.69.054320"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-80240-8"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-3276(08)60616-4"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00527713"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01119615"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1063\/1.4718427"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1080\/00268976.2013.812254"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044451719-7\/50050-0"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.5.50"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2012035"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2013075"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0237-3"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1063\/1.1732596"},{"key":"atypb20","series-title":"Lecture Notes In Math.","volume-title":"Regularity and Approximability of Electronic Wavefunctions","author":"Yserentant H.","year":"2000"},{"key":"atypb21","unstructured":"E. Zarantonello,\n                      Solving Functional Equations by Contractive Averaging\n                      , Tech. 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