{"id":"https://openalex.org/W2144917506","doi":"https://doi.org/10.1137/s0895479899359837","title":"Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems","display_name":"Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2144917506","doi":"https://doi.org/10.1137/s0895479899359837","mag":"2144917506"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479899359837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899359837","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059791596","display_name":"Fran\u00e7oise Tisseur","orcid":"https://orcid.org/0000-0002-1011-2570"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Fran\u00e7oise Tisseur","raw_affiliation_strings":["Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5059791596"],"corresponding_institution_ids":["https://openalex.org/I4210131439"],"apc_list":null,"apc_paid":null,"fwci":2.7472,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.90481087,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"4","first_page":"1038","last_page":"1057"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7890139222145081},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.7717806696891785},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7225723266601562},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6988359093666077},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6943390965461731},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6520352363586426},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6120710372924805},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.598414421081543},{"id":"https://openalex.org/keywords/iterative-refinement","display_name":"Iterative refinement","score":0.5602660179138184},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5369470119476318},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.4843098223209381},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4691169559955597},{"id":"https://openalex.org/keywords/machine-epsilon","display_name":"Machine epsilon","score":0.46857950091362},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41701412200927734},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.3991534411907196},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.395469069480896},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12781912088394165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7890139222145081},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7717806696891785},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7225723266601562},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6988359093666077},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6943390965461731},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6520352363586426},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6120710372924805},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.598414421081543},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.5602660179138184},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5369470119476318},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.4843098223209381},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4691169559955597},{"id":"https://openalex.org/C203739276","wikidata":"https://www.wikidata.org/wiki/Q1780355","display_name":"Machine epsilon","level":2,"score":0.46857950091362},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41701412200927734},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.3991534411907196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.395469069480896},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12781912088394165},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s0895479899359837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899359837","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:979","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:hdl:10068/647499","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/647499","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.3","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.3","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.ma.man.ac.uk/979/01/tisseur3.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/232b71ca-e379-45f0-bfd1-bb335e86327b","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/232b71ca-e379-45f0-bfd1-bb335e86327b","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Tisseur, F 2001, 'Newton's method in floating point arithmetic and iterative refinement of generalized eigenvalue problems', SIAM Journal on Matrix Analysis and Applications, vol. 22, no. 4, pp. 1038-1057. https://doi.org/10.1137/S0895479899359837","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.atira.dk:publications/232b71ca-e379-45f0-bfd1-bb335e86327b","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/newtons-method-in-floating-point-arithmetic-and-iterative-refinement-of-generalized-eigenvalue-problems(232b71ca-e379-45f0-bfd1-bb335e86327b).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Tisseur, F 2001, 'Newton's method in floating point arithmetic and iterative refinement of generalized eigenvalue problems', SIAM Journal on Matrix Analysis and Applications, vol. 22, no. 4, pp. 1038-1057. https://doi.org/10.1137/S0895479899359837","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W82751690","https://openalex.org/W202654784","https://openalex.org/W1492579554","https://openalex.org/W1965210108","https://openalex.org/W1966287322","https://openalex.org/W1975721804","https://openalex.org/W1981745143","https://openalex.org/W1984938247","https://openalex.org/W1987035720","https://openalex.org/W1988201922","https://openalex.org/W2017711521","https://openalex.org/W2020804487","https://openalex.org/W2022296788","https://openalex.org/W2026927759","https://openalex.org/W2032875563","https://openalex.org/W2044008067","https://openalex.org/W2045651847","https://openalex.org/W2050481923","https://openalex.org/W2052926498","https://openalex.org/W2053489736","https://openalex.org/W2068484625","https://openalex.org/W2078126355","https://openalex.org/W2104849640","https://openalex.org/W2113606817","https://openalex.org/W2140715711","https://openalex.org/W2163336887","https://openalex.org/W2168775671","https://openalex.org/W2314981175","https://openalex.org/W2798909945","https://openalex.org/W3022909171","https://openalex.org/W4253532698","https://openalex.org/W4380434592"],"related_works":["https://openalex.org/W2350788688","https://openalex.org/W2937715180","https://openalex.org/W2380062341","https://openalex.org/W4297921956","https://openalex.org/W2951861326","https://openalex.org/W2259043954","https://openalex.org/W3094698614","https://openalex.org/W2387535608","https://openalex.org/W1985487460","https://openalex.org/W2144917506"],"abstract_inverted_index":{"We":[0,32,58],"examine":[1],"the":[2,18,23,29,34,38,42,54,71],"behavior":[3],"of":[4,17,22,28,41,76],"Newton's":[5,64],"method":[6,65],"in":[7,15],"floating":[8],"point":[9],"arithmetic,":[10],"allowing":[11],"for":[12,53],"extended":[13],"precision":[14],"computation":[16],"residual,":[19],"inaccurate":[20],"evaluation":[21],"Jacobian":[24],"and":[25,37,73],"unstable":[26],"solution":[27],"linear":[30],"systems.":[31],"bound":[33],"limiting":[35],"accuracy":[36],"smallest":[39],"norm":[40],"residual.":[43],"The":[44],"application":[45],"that":[46,60],"motivates":[47],"this":[48],"work":[49],"is":[50],"iterative":[51,61],"refinement":[52,62],"generalized":[55],"eigenvalue":[56],"problem.":[57],"show":[59],"by":[63],"can":[66],"be":[67],"used":[68],"to":[69],"improve":[70],"forward":[72],"backward":[74],"errors":[75],"computed":[77],"eigenpairs.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-05T09:01:59.212387","created_date":"2025-10-10T00:00:00"}
