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Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDL\n                    <jats:sup>T<\/jats:sup>\n                    factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude.\n                  <\/jats:p>","DOI":"10.1137\/050637649","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:29:50Z","timestamp":1156433390000},"page":"963-983","source":"Crossref","is-referenced-by-count":26,"title":["On Large-Scale Diagonalization Techniques for the Anderson Model of Localization"],"prefix":"10.1137","volume":"28","author":[{"given":"Olaf","family":"Schenk","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Bollh\u00f6fer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rudolf A.","family":"R\u00f6mer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894278952"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.109.1492"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.33.7310"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2004.09.026"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7176"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599361308"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/040608374"},{"key":"R9","unstructured":"M. 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