{"id":"https://openalex.org/W7131615782","doi":"https://doi.org/10.48550/arxiv.2602.21974","title":"Subspace gradient descent method for linear tensor equations","display_name":"Subspace gradient descent method for linear tensor equations","publication_year":2026,"publication_date":"2026-02-25","ids":{"openalex":"https://openalex.org/W7131615782","doi":"https://doi.org/10.48550/arxiv.2602.21974"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.21974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.21974","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.21974","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036115322","display_name":"Martina Iannacito","orcid":"https://orcid.org/0000-0003-3354-2538"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iannacito, Martina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093868535","display_name":"Lorenzo Piccinini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piccinini, Lorenzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081841768","display_name":"Valeria Simoncini","orcid":"https://orcid.org/0000-0003-0795-5865"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simoncini, Valeria","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.014399999752640724,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.002400000113993883,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6899999976158142},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5857999920845032},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5795000195503235},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.5321999788284302},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5166000127792358},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.4740999937057495},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.42649999260902405},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.420199990272522},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.38429999351501465},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.37689998745918274}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7570000290870667},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6899999976158142},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5857999920845032},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5795000195503235},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.5321999788284302},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5166000127792358},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4771000146865845},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.4740999937057495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.42649999260902405},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.420199990272522},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.35420000553131104},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.3499999940395355},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.29840001463890076},{"id":"https://openalex.org/C90952326","wikidata":"https://www.wikidata.org/wiki/Q3650511","display_name":"Tensor calculus","level":4,"score":0.2971999943256378},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.2962999939918518},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25589999556541443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.21974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.21974","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.21974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.21974","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,96],"numerical":[1],"solution":[2],"of":[3,62,98,109,129],"algebraic":[4],"tensor":[5,31,63],"equations":[6,32,113],"is":[7,18,56,68,101],"a":[8,59],"largely":[9],"open":[10],"and":[11,20,50,88],"challenging":[12],"task.":[13],"Assuming":[14],"that":[15,33],"the":[16,35,65,85,119,127,130],"operator":[17],"symmetric":[19],"positive":[21],"definite,":[22],"we":[23],"propose":[24],"two":[25],"new":[26],"gradient-descent":[27],"type":[28],"methods":[29],"for":[30],"generalize":[34],"recently":[36],"proposed":[37,131],"Subspace":[38],"Conjugate":[39],"Gradient":[40],"(SS-CG),":[41],"D.":[42],"Palitta":[43],"et":[44],"al,":[45],"SIAM":[46],"J.":[47],"Matrix":[48],"Analysis":[49],"Appl":[51],"(2025).":[52],"As":[53],"our":[54,99],"interest":[55],"mainly":[57],"in":[58,80],"modest":[60],"number":[61],"modes,":[64],"Tucker":[66],"format":[67],"used":[69],"to":[70,83,93],"efficiently":[71],"represent":[72],"low-rank":[73],"tensors.":[74],"Moreover,":[75],"mixed-precision":[76],"strategies":[77,100],"are":[78,91],"employed":[79],"certain":[81],"subtasks":[82],"improve":[84],"memory":[86],"usage,":[87],"different":[89],"preconditioners":[90],"applied":[92],"enhance":[94],"convergence.":[95],"potential":[97],"illustrated":[102],"by":[103],"experimental":[104],"results":[105],"on":[106],"tensor-oriented":[107],"discretizations":[108],"three-dimensional":[110],"partial":[111],"differential":[112],"with":[114,118],"separable":[115],"coefficients.":[116],"Comparisons":[117],"state-of-the-art":[120],"Alternating":[121],"Minimal":[122],"Energy":[123],"(AMEn)":[124],"algorithm":[125],"confirm":[126],"competitiveness":[128],"strategies.":[132]},"counts_by_year":[],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2026-02-27T00:00:00"}