{"id":"https://openalex.org/W3014098867","doi":"https://doi.org/10.1515/comp-2020-0012","title":"Preconditioned Subspace Descent Method for Nonlinear Systems of Equations","display_name":"Preconditioned Subspace Descent Method for Nonlinear Systems of Equations","publication_year":2020,"publication_date":"2020-03-20","ids":{"openalex":"https://openalex.org/W3014098867","doi":"https://doi.org/10.1515/comp-2020-0012","mag":"3014098867"},"language":"en","primary_location":{"id":"doi:10.1515/comp-2020-0012","is_oa":true,"landing_page_url":"https://doi.org/10.1515/comp-2020-0012","pdf_url":"https://www.degruyter.com/document/doi/10.1515/comp-2020-0012/pdf","source":{"id":"https://openalex.org/S4210177004","display_name":"Open Computer Science","issn_l":"2299-1093","issn":["2299-1093"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyter.com/document/doi/10.1515/comp-2020-0012/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075272796","display_name":"Igor Kaporin","orcid":"https://orcid.org/0000-0002-1451-1632"},"institutions":[{"id":"https://openalex.org/I2801535751","display_name":"Dorodnitsyn Computing Centre","ror":"https://ror.org/01vgda714","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801535751","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Igor Kaporin","raw_affiliation_strings":["Dorodnicyn Computer Center of FRC CSC RAS,Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dorodnicyn Computer Center of FRC CSC RAS,Moscow, Russia","institution_ids":["https://openalex.org/I2801535751"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075272796"],"corresponding_institution_ids":["https://openalex.org/I2801535751"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":1.568,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79967009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"1","first_page":"71","last_page":"81"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9959999918937683,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9850000143051147,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7775429487228394},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6582623720169067},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5892797112464905},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5526870489120483},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.512201726436615},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5109788179397583},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.495613694190979},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4550841450691223},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4334036409854889},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.42583978176116943},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.41903048753738403},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.41753190755844116},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3757505416870117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35675978660583496},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2452954351902008},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17642328143119812},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08147779107093811}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7775429487228394},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6582623720169067},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5892797112464905},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5526870489120483},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.512201726436615},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5109788179397583},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.495613694190979},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4550841450691223},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4334036409854889},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.42583978176116943},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.41903048753738403},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.41753190755844116},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3757505416870117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35675978660583496},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2452954351902008},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17642328143119812},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08147779107093811},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/comp-2020-0012","is_oa":true,"landing_page_url":"https://doi.org/10.1515/comp-2020-0012","pdf_url":"https://www.degruyter.com/document/doi/10.1515/comp-2020-0012/pdf","source":{"id":"https://openalex.org/S4210177004","display_name":"Open Computer Science","issn_l":"2299-1093","issn":["2299-1093"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8c3e64c8df5b46869d97efcf63e65aee","is_oa":true,"landing_page_url":"https://doaj.org/article/8c3e64c8df5b46869d97efcf63e65aee","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Open Computer Science, Vol 10, Iss 1, Pp 71-81 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/comp-2020-0012","is_oa":true,"landing_page_url":"https://doi.org/10.1515/comp-2020-0012","pdf_url":"https://www.degruyter.com/document/doi/10.1515/comp-2020-0012/pdf","source":{"id":"https://openalex.org/S4210177004","display_name":"Open Computer Science","issn_l":"2299-1093","issn":["2299-1093"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3014098867.pdf","grobid_xml":"https://content.openalex.org/works/W3014098867.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1576571322","https://openalex.org/W1601946875","https://openalex.org/W1964974767","https://openalex.org/W1969811075","https://openalex.org/W1978347765","https://openalex.org/W2018014435","https://openalex.org/W2019865138","https://openalex.org/W2035002995","https://openalex.org/W2035476608","https://openalex.org/W2042686672","https://openalex.org/W2151163324","https://openalex.org/W2158235460","https://openalex.org/W2313672321","https://openalex.org/W2316564661","https://openalex.org/W2582025857","https://openalex.org/W2586678101","https://openalex.org/W2613058787","https://openalex.org/W2810507125","https://openalex.org/W3000051334","https://openalex.org/W3093790569","https://openalex.org/W4234591907","https://openalex.org/W4234964427","https://openalex.org/W4252318916"],"related_works":["https://openalex.org/W3091226915","https://openalex.org/W2492745391","https://openalex.org/W2951682359","https://openalex.org/W1967348596","https://openalex.org/W2527533633","https://openalex.org/W2092886819","https://openalex.org/W2116573255","https://openalex.org/W2119553411","https://openalex.org/W1585725267","https://openalex.org/W2575167716"],"abstract_inverted_index":{"Abstract":[0],"Nonlinear":[1],"least":[2],"squares":[3],"iterative":[4],"solver":[5],"is":[6,15,68,88],"considered":[7],"for":[8,90,140],"real-valued":[9],"sufficiently":[10],"smooth":[11],"functions.":[12],"The":[13,35,50,96],"algorithm":[14],"based":[16,52],"on":[17,27,53],"successive":[18],"solution":[19],"of":[20,23,30,37,47,56,75,98,124,135],"orthogonal":[21],"projections":[22],"the":[24,38,44,48,54,57,66,72,76,84,91],"linearized":[25],"equation":[26],"a":[28],"sequence":[29],"appropriately":[31],"chosen":[32],"low-dimensional":[33],"subspaces.":[34],"bases":[36],"latter":[39],"are":[40,101],"constructed":[41],"using":[42],"only":[43,105],"first-order":[45],"derivatives":[46],"function.":[49],"technique":[51],"concept":[55],"limiting":[58],"stepsize":[59],"along":[60],"normalized":[61],"direction":[62],"(developed":[63],"earlier":[64],"by":[65],"author)":[67],"used":[69],"to":[70,86],"guarantee":[71],"monotone":[73],"decrease":[74],"nonlinear":[77,137],"residual":[78,94],"norm.":[79],"Under":[80],"rather":[81],"mild":[82],"conditions,":[83],"convergence":[85],"zero":[87],"proved":[89],"gradient":[92],"and":[93,113,126],"norms.":[95],"results":[97],"numerical":[99],"testing":[100],"presented,":[102],"including":[103],"not":[104],"small-sized":[106],"standard":[107],"test":[108],"problems,":[109],"but":[110],"also":[111],"larger":[112],"harder":[114],"examples,":[115],"such":[116],"as":[117,130,132],"algebraic":[118],"problems":[119,139],"associated":[120],"with":[121],"canonical":[122],"decomposition":[123],"dense":[125],"sparse":[127],"3D":[128],"tensors":[129],"well":[131],"finite-difference":[133],"discretizations":[134],"2D":[136],"boundary":[138],"2nd":[141],"order":[142],"partial":[143],"differential":[144],"equations.":[145]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-04-10T00:00:00"}