{"id":"https://openalex.org/W4410028974","doi":"https://doi.org/10.3390/sym17050664","title":"Numerical Methods Combining Symmetry and Sparsity for the Calculation of Homogeneous Polynomials Defined by Tensors","display_name":"Numerical Methods Combining Symmetry and Sparsity for the Calculation of Homogeneous Polynomials Defined by Tensors","publication_year":2025,"publication_date":"2025-04-27","ids":{"openalex":"https://openalex.org/W4410028974","doi":"https://doi.org/10.3390/sym17050664"},"language":"en","primary_location":{"id":"doi:10.3390/sym17050664","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17050664","pdf_url":"https://www.mdpi.com/2073-8994/17/5/664/pdf?version=1745918428","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/5/664/pdf?version=1745918428","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100458348","display_name":"Ting Zhang","orcid":"https://orcid.org/0000-0003-0326-6528"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ting Zhang","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100458348"],"corresponding_institution_ids":["https://openalex.org/I92403157"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1140873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"5","first_page":"664","last_page":"664"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9902999997138977,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9562000036239624,"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/homogeneous","display_name":"Homogeneous","score":0.7078119516372681},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6699879765510559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5003204345703125},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4226230978965759},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3479710519313812},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3337913751602173},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20497864484786987},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17859897017478943}],"concepts":[{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.7078119516372681},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6699879765510559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5003204345703125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4226230978965759},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3479710519313812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3337913751602173},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20497864484786987},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17859897017478943}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17050664","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17050664","pdf_url":"https://www.mdpi.com/2073-8994/17/5/664/pdf?version=1745918428","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17050664","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17050664","pdf_url":"https://www.mdpi.com/2073-8994/17/5/664/pdf?version=1745918428","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410028974.pdf","grobid_xml":"https://content.openalex.org/works/W4410028974.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W175892734","https://openalex.org/W1602295990","https://openalex.org/W1656443807","https://openalex.org/W1942532907","https://openalex.org/W1958607180","https://openalex.org/W2090208105","https://openalex.org/W2151293435","https://openalex.org/W2154650988","https://openalex.org/W2204354727","https://openalex.org/W2222111999","https://openalex.org/W2266798071","https://openalex.org/W2582681631","https://openalex.org/W2749459105","https://openalex.org/W2785941732","https://openalex.org/W2787889286","https://openalex.org/W2793479357","https://openalex.org/W2902323448","https://openalex.org/W2964083650","https://openalex.org/W2966845367","https://openalex.org/W2967514193","https://openalex.org/W2968579382","https://openalex.org/W3026386065","https://openalex.org/W3088555464","https://openalex.org/W3188368100","https://openalex.org/W4213158988","https://openalex.org/W4226061425","https://openalex.org/W4306404585","https://openalex.org/W4313268854","https://openalex.org/W4376129296","https://openalex.org/W4390662288","https://openalex.org/W4390777162","https://openalex.org/W4408576787","https://openalex.org/W6756797451"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1598955744","https://openalex.org/W4285167822","https://openalex.org/W2951710344","https://openalex.org/W2204136089","https://openalex.org/W1917349875","https://openalex.org/W2144602163","https://openalex.org/W4384111961","https://openalex.org/W2127985649","https://openalex.org/W4249202279"],"abstract_inverted_index":{"The":[0],"homogeneous":[1,70,114],"polynomial":[2,48],"defined":[3,50],"by":[4,51,182],"a":[5,52,76,118,142,155],"tensor,":[6,53,133],"Axm\u22121":[7],"for":[8,92,180],"x\u2208Rn,":[9],"has":[10],"been":[11],"used":[12],"in":[13,17,109,190],"many":[14],"recent":[15],"problems":[16],"the":[18,26,61,66,90,97,104,110,122,126,131,136,151,168,171,183,197],"context":[19],"of":[20,47,69,99,106,113,125,170,199],"tensor":[21,27,30,32,35,39,124,128,184],"analysis":[22],"and":[23,43,64,202],"optimization,":[24],"including":[25],"eigenvalue":[28,36],"problem,":[29,34,38,42],"equation,":[31],"complementary":[33,37],"variational":[40],"inequality":[41],"least":[44],"element":[45],"problem":[46],"inequalities":[49],"among":[54],"others.":[55],"However,":[56],"conventional":[57],"computation":[58],"methods":[59,94],"use":[60,181],"definition":[62],"directly":[63],"neglect":[65],"structural":[67],"characteristics":[68],"polynomials":[71],"involving":[72],"tensors,":[73],"leading":[74],"to":[75,95,129,148],"high":[77],"computational":[78,137,152,188],"burden":[79],"(especially":[80],"when":[81],"considering":[82,103],"iterative":[83],"algorithms":[84,179],"or":[85],"large-scale":[86],"problems).":[87],"This":[88],"motivates":[89],"need":[91],"efficient":[93],"reduce":[96,150],"complexity":[98],"relevant":[100],"algorithms.":[101],"First,":[102],"symmetry":[105],"each":[107],"monomial":[108],"canonical":[111],"basis":[112],"polynomials,":[115],"we":[116,140],"propose":[117,141],"calculation":[119,143,198],"method":[120,144],"using":[121],"merge":[123],"involved":[127],"replace":[130],"original":[132],"thus":[134],"reducing":[135],"cost.":[138,153],"Second,":[139],"that":[145,158],"combines":[146],"sparsity":[147],"further":[149],"Finally,":[154],"simplified":[156],"algorithm":[157],"avoids":[159],"duplicate":[160],"calculations":[161],"is":[162],"proposed.":[163],"Extensive":[164],"numerical":[165],"experiments":[166],"demonstrate":[167],"effectiveness":[169],"proposed":[172],"methods,":[173],"which":[174],"can":[175],"be":[176],"embedded":[177],"into":[178],"optimization":[185],"community,":[186],"improving":[187],"efficiency":[189],"magnetic":[191],"resonance":[192],"imaging,":[193],"n-person":[194],"non-cooperative":[195],"games,":[196],"molecular":[200],"orbitals,":[201],"so":[203],"on.":[204]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}