{"id":"https://openalex.org/W1972947894","doi":"https://doi.org/10.1007/s002110100355","title":"Riccati-based preconditioner for computing invariant subspaces of large matrices","display_name":"Riccati-based preconditioner for computing invariant subspaces of large matrices","publication_year":2002,"publication_date":"2002-07-01","ids":{"openalex":"https://openalex.org/W1972947894","doi":"https://doi.org/10.1007/s002110100355","mag":"1972947894"},"language":"en","primary_location":{"id":"doi:10.1007/s002110100355","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002110100355","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5086203082","display_name":"Micka\u00ebl Robb\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"M. Robb\u00e9","raw_affiliation_strings":["Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France; e-mail: {robbe,sadkane}@univ-brest.fr\n, , , , , , FR","Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France","e-mail: {robbe,sadkane}@univ-brest.fr\n, , FR"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France; e-mail: {robbe,sadkane}@univ-brest.fr\n, , , , , , FR","institution_ids":["https://openalex.org/I161929037"]},{"raw_affiliation_string":"Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I3019441195"]},{"raw_affiliation_string":"e-mail: {robbe,sadkane}@univ-brest.fr\n, , FR","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066895480","display_name":"Miloud Sadkane","orcid":"https://orcid.org/0000-0002-7712-7048"},"institutions":[{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Sadkane","raw_affiliation_strings":["Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France; e-mail: {robbe,sadkane}@univ-brest.fr\n, , , , , , FR","e-mail: {robbe,sadkane}@univ-brest.fr\n, , FR","Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France; e-mail: {robbe,sadkane}@univ-brest.fr\n, , , , , , FR","institution_ids":["https://openalex.org/I161929037"]},{"raw_affiliation_string":"e-mail: {robbe,sadkane}@univ-brest.fr\n, , FR","institution_ids":[]},{"raw_affiliation_string":"Universit\u00e9 de Bretagne Occidentale, D\u00e9partement de Math\u00e9matiques, 6, Av. Le Gorgeu, BP 809, 29285 Brest Cedex, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I3019441195"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086203082"],"corresponding_institution_ids":["https://openalex.org/I161929037","https://openalex.org/I3019441195"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6977,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67152142,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"92","issue":"1","first_page":"129","last_page":"159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8114094138145447},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.7741349935531616},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.661230206489563},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6255158185958862},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.6063250303268433},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.6023521423339844},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5858094096183777},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49092867970466614},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.45878416299819946},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.45139098167419434},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.44944053888320923},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.423078328371048},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4132775664329529},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27071383595466614},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.26403284072875977},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25432121753692627},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.2519407570362091},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2332378625869751},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.18353262543678284},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10324603319168091}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8114094138145447},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.7741349935531616},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.661230206489563},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6255158185958862},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.6063250303268433},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.6023521423339844},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5858094096183777},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49092867970466614},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.45878416299819946},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.45139098167419434},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44944053888320923},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.423078328371048},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4132775664329529},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27071383595466614},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.26403284072875977},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25432121753692627},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2519407570362091},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2332378625869751},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.18353262543678284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10324603319168091},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s002110100355","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002110100355","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W658559791","https://openalex.org/W1506342804","https://openalex.org/W1514113870","https://openalex.org/W1563653928","https://openalex.org/W1575147392","https://openalex.org/W1600349401","https://openalex.org/W1973516374","https://openalex.org/W1976767533","https://openalex.org/W2041894797","https://openalex.org/W2083911735","https://openalex.org/W2086160340","https://openalex.org/W2090963365","https://openalex.org/W2116732229"],"related_works":["https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W2096454229","https://openalex.org/W2042199958","https://openalex.org/W2103149966","https://openalex.org/W2177482563","https://openalex.org/W2120298265","https://openalex.org/W2464766188","https://openalex.org/W2016008514","https://openalex.org/W3160810049"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}