{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/68189"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/68189","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method","abstract":"Two algorithms of use in sparse matrix computation are studied. The rounding errors of the computational Lanczos algorithm are examined in order to account for the differences between the ideal and the machine-operator quantities. The observed behavior of these errors is explained by means of a formal error analysis which relates the errors to properties of the matrix tridiagonalization problem solved by the algorithm. An investigation of the orthogonal polynomials associated with the algorithm partially explains the observed phenomena.","abstract_html":"Two algorithms of use in sparse matrix computation are studied. The rounding errors of the computational Lanczos algorithm are examined in order to account for the differences between the ideal and the machine-operator quantities. The observed behavior of these errors is explained by means of a formal error analysis which relates the errors to properties of the matrix tridiagonalization problem solved by the algorithm. 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The rounding errors of the computational Lanczos algorithm are examined in order to account for the differences between the ideal and the machine-operator quantities. The observed behavior of these errors is explained by means of a formal error analysis which relates the errors to properties of the matrix tridiagonalization problem solved by the algorithm. An investigation of the orthogonal polynomials associated with the algorithm partially explains the observed phenomena.","For Richardson's method of solving systems of linear equations, the associated uniform approximation problem is taken as a particular case of a more general problem. The solutions to the latter are characterized. A version of the algorithm of Remez is shown to solve these problems.","Made available in DSpace on 2014-12-14T13:09:51Z (GMT). No. of bitstreams: 1 8203472.pdf: 4954715 bytes, checksum: 3cee9630d78b0cc6ba5ac3bc1611f509 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 68367 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","194 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."]},{"key":"dc:title","label":"Title","values":["Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method"]}]}],"canonical_facts":{"dc:creator":["Grcar, Joseph Frank"],"dc:date":["2014-12-14T13:09:51Z","10000-01-01","1981"],"dc:description":["Two algorithms of use in sparse matrix computation are studied. The rounding errors of the computational Lanczos algorithm are examined in order to account for the differences between the ideal and the machine-operator quantities. The observed behavior of these errors is explained by means of a formal error analysis which relates the errors to properties of the matrix tridiagonalization problem solved by the algorithm. An investigation of the orthogonal polynomials associated with the algorithm partially explains the observed phenomena.","For Richardson's method of solving systems of linear equations, the associated uniform approximation problem is taken as a particular case of a more general problem. The solutions to the latter are characterized. A version of the algorithm of Remez is shown to solve these problems.","Made available in DSpace on 2014-12-14T13:09:51Z (GMT). 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