{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/52945"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/52945","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Reusing and Updating Preconditioners for Sequences of Matrices","abstract":"For sequences of related linear systems, the computation of a preconditioner for every system can be expensive. Often a fixed preconditioner is used, but this may not be effective as the matrix changes. This research examines the benefits of both reusing and recycling preconditioners, with special focus on ILUTP and factorized sparse approximate inverses and proposes an update that we refer to as a sparse approximate map or SAM update. Analysis of the residual and eigenvalues of the map will be provided. 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Often a fixed preconditioner is used, but this may not be effective as the matrix changes. This research examines the benefits of both reusing and recycling preconditioners, with special focus on ILUTP and factorized sparse approximate inverses and proposes an update that we refer to as a sparse approximate map or SAM update. Analysis of the residual and eigenvalues of the map will be provided. 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