{"id":"https://openalex.org/W4406617847","doi":"https://doi.org/10.1007/s00211-025-01451-0","title":"Riemannian acceleration with preconditioning for symmetric eigenvalue problems","display_name":"Riemannian acceleration with preconditioning for symmetric eigenvalue problems","publication_year":2025,"publication_date":"2025-01-20","ids":{"openalex":"https://openalex.org/W4406617847","doi":"https://doi.org/10.1007/s00211-025-01451-0"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-025-01451-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01451-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01451-0.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01451-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101841881","display_name":"Nian Shao","orcid":"https://orcid.org/0009-0009-5755-5350"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Nian Shao","raw_affiliation_strings":["Institute of Mathematics, EPFL, 1015, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, EPFL, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100693236","display_name":"Wenbin Chen","orcid":"https://orcid.org/0000-0001-8305-0764"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenbin Chen","raw_affiliation_strings":["School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101841881"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.0681,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.89695028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"157","issue":"1","first_page":"307","last_page":"354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9990000128746033,"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":0.9990000128746033,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8088971376419067},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.662152886390686},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6502636075019836},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49319857358932495},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4744597375392914},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3371328115463257},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.12352743744850159},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06663459539413452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8088971376419067},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.662152886390686},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6502636075019836},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49319857358932495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4744597375392914},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3371328115463257},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12352743744850159},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06663459539413452},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-025-01451-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01451-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01451-0.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:20.500.14299/245831","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/245831","pdf_url":"https://infoscience.epfl.ch/bitstreams/0fd95f5f-fc0a-4836-bce1-39448ceb95ff/download","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"doi:10.1007/s00211-025-01451-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-025-01451-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-025-01451-0.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2157888273","display_name":null,"funder_award_id":"12241101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3268513699","display_name":null,"funder_award_id":"12071090","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G373900780","display_name":null,"funder_award_id":"12471369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5161677271","display_name":null,"funder_award_id":"12471","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406617847.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W86404423","https://openalex.org/W597568752","https://openalex.org/W1548589512","https://openalex.org/W1964551934","https://openalex.org/W1974907720","https://openalex.org/W1981276685","https://openalex.org/W1981792545","https://openalex.org/W2023722580","https://openalex.org/W2044333641","https://openalex.org/W2045512849","https://openalex.org/W2051142108","https://openalex.org/W2059586807","https://openalex.org/W2066910699","https://openalex.org/W2076995010","https://openalex.org/W2100556411","https://openalex.org/W2106173883","https://openalex.org/W2109443444","https://openalex.org/W2127447444","https://openalex.org/W2139039544","https://openalex.org/W2142184851","https://openalex.org/W2167732364","https://openalex.org/W2480854438","https://openalex.org/W2785206729","https://openalex.org/W2808632227","https://openalex.org/W2896405912","https://openalex.org/W3037096902","https://openalex.org/W3101845474","https://openalex.org/W3105832093","https://openalex.org/W3105971472","https://openalex.org/W3110968468","https://openalex.org/W3124961975","https://openalex.org/W3181590451","https://openalex.org/W3197024903","https://openalex.org/W3204708751","https://openalex.org/W3205832882","https://openalex.org/W4205293427","https://openalex.org/W4230094279","https://openalex.org/W4232240772","https://openalex.org/W4234194857","https://openalex.org/W4301491118","https://openalex.org/W4321481114","https://openalex.org/W4323539420","https://openalex.org/W4366404946","https://openalex.org/W4403208450","https://openalex.org/W4406038114"],"related_works":["https://openalex.org/W2565094479","https://openalex.org/W2390829436","https://openalex.org/W1989791859","https://openalex.org/W602859758","https://openalex.org/W1971289376","https://openalex.org/W2379101322","https://openalex.org/W1992553864","https://openalex.org/W2776207444","https://openalex.org/W2088932963","https://openalex.org/W4285308861"],"abstract_inverted_index":{"Abstract":[0],"The":[1,145],"analysis":[2,78],"of":[3,7,79,94,126],"the":[4,34,46,59,80,120],"acceleration":[5,61],"behavior":[6],"gradient-based":[8],"eigensolvers":[9],"with":[10,62],"preconditioning":[11,26,63],"presents":[12],"a":[13,22,32,91],"substantial":[14],"theoretical":[15,71,169],"challenge.":[16],"In":[17],"this":[18],"work,":[19],"we":[20],"present":[21],"novel":[23],"framework":[24],"for":[25,40,53,65,83],"on":[27],"Riemannian":[28,49,54,60],"manifolds":[29],"and":[30,164],"introduce":[31],"metric,":[33],"leading":[35],"angle,":[36],"to":[37,57,73],"evaluate":[38],"preconditioners":[39],"symmetric":[41,66],"eigenvalue":[42,67,85],"problems.":[43],"We":[44],"extend":[45],"locally":[47],"optimal":[48],"accelerated":[50],"gradient":[51],"method":[52],"convex":[55],"optimization":[56],"develop":[58],"(RAP)":[64],"problems,":[68],"thereby":[69],"providing":[70],"evidence":[72],"support":[74],"its":[75],"acceleration.":[76],"Our":[77],"Schwarz":[81],"preconditioner":[82],"elliptic":[84],"problems":[86],"demonstrates":[87],"that":[88],"RAP":[89],"achieves":[90],"convergence":[92],"rate":[93,125],"$$1-C\\kappa":[95,127],"^{-1/2}$$":[96,149],"<mml:math":[97,129,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[98,130,151],"<mml:mrow>":[99,105,131,137,154],"<mml:mn>1</mml:mn>":[100,107,132,139,156],"<mml:mo>-</mml:mo>":[101,106,133,138,155],"<mml:mi>C</mml:mi>":[102,134],"<mml:msup>":[103,135,152],"<mml:mi>\u03ba</mml:mi>":[104,136,153],"<mml:mo>/</mml:mo>":[108,157],"<mml:mn>2</mml:mn>":[109,158],"</mml:mrow>":[110,112,140,142,159],"</mml:msup>":[111,141,160],"</mml:math>":[113,143,161],",":[114],"which":[115],"is":[116,162],"an":[117],"improvement":[118],"over":[119],"preconditioned":[121],"steepest":[122],"descent":[123],"method\u2019s":[124],"^{-1}$$":[128],".":[144],"exponent":[146],"in":[147],"$$\\kappa":[148],"sharp,":[163],"numerical":[165],"experiments":[166],"confirm":[167],"our":[168],"findings.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}