{"id":"https://openalex.org/W6910764636","doi":"https://doi.org/10.48550/arxiv.2507.22634","title":"Tropical solution of discrete best approximation problems","display_name":"Tropical solution of discrete best approximation problems","publication_year":2025,"publication_date":"2025-07-30","ids":{"openalex":"https://openalex.org/W6910764636","doi":"https://doi.org/10.48550/arxiv.2507.22634"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2507.22634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.22634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2507.22634","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Krivulin, Nikolai","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Krivulin, Nikolai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"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":true,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9929999709129333,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9929999709129333,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.0013000000035390258,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0010999999940395355,"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/monomial","display_name":"Monomial","score":0.5626999735832214},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5616000294685364},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48019999265670776},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45410001277923584},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.37049999833106995},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.3610000014305115},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3596000075340271},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.31520000100135803}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8855000138282776},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.5626999735832214},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5616000294685364},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45410001277923584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45100000500679016},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31520000100135803},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.31520000100135803},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.29440000653266907},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2816999852657318},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.26649999618530273},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2556999921798706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2507.22634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.22634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2507.22634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.22634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"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":{"We":[0,152],"consider":[1],"discrete":[2],"best":[3],"approximation":[4,68,107,198,229,258],"problems":[5,285],"in":[6,64,79,90,231,271],"the":[7,16,41,67,72,80,84,88,91,100,123,127,131,142,147,169,177,189,210,267,284],"setting":[8],"of":[9,20,29,32,62,93,108,149,160,168,191,233,255,259,275],"tropical":[10,39,95],"algebra,":[11],"which":[12,193,249],"is":[13,43,184],"concerned":[14],"with":[15,23,112,138,186,212,239],"theory":[17],"and":[18,57,74,126,175,197,244,277],"application":[19],"algebraic":[21],"systems":[22],"idempotent":[24],"operations.":[25],"Given":[26],"a":[27,38,94,109,136,158,272,279],"set":[28],"input--output":[30],"pairs":[31],"an":[33,46,106,154,172,213,218,228,252],"unknown":[34,113,143,150],"function":[35,49,86],"defined":[36,241],"on":[37,115,141,217],"semifield,":[40],"problem":[42,230,254],"to":[44,82,87,122,130,171,188,251,283],"determine":[45],"approximating":[47],"rational":[48,85],"formed":[50],"by":[51,146,163,202,208],"two":[52],"Puiseux":[53],"polynomials":[54,81],"as":[55,242,246],"numerator":[56,124],"denominator.":[58,132],"With":[59],"specified":[60],"numbers":[61],"monomials":[63],"both":[65,116,200],"polynomials,":[66],"aims":[69],"at":[70],"evaluating":[71],"exponent":[73],"coefficient":[75],"for":[76,227],"each":[77],"monomial":[78],"fit":[83],"data":[89],"sense":[92],"distance":[96],"function.":[97],"To":[98,222],"solve":[99],"problem,":[101],"we":[102,224],"transform":[103],"it":[104],"into":[105],"vector":[110,148,190,196],"equation":[111,170,182],"vectors":[114],"sides,":[117],"where":[118],"one":[119,166],"side":[120,129,134,167,179],"corresponds":[121,250],"polynomial":[125],"other":[128,178],"Each":[133,181],"involves":[135],"matrix":[137],"entries":[139],"dependent":[140],"exponents,":[144],"multiplied":[145],"coefficients.":[151],"propose":[153],"algorithm":[155,269],"that":[156],"constructs":[157],"series":[159],"approximate":[161],"solutions":[162],"alternately":[164],"fixing":[165],"already-found":[173],"result":[174],"leaving":[176],"intact.":[180],"obtained":[183],"approximated":[185],"respect":[187],"coefficients,":[192],"yields":[194],"this":[195],"error,":[199],"parameterized":[201],"exponents.":[203],"The":[204],"exponents":[205],"are":[206],"found":[207],"minimizing":[209],"error":[211],"optimization":[214],"procedure":[215],"based":[216],"agglomerative":[219],"clustering":[220],"technique.":[221],"illustrate,":[223],"present":[225],"results":[226],"terms":[232],"max-plus":[234],"algebra":[235],"(a":[236],"real":[237,260],"semifield":[238],"addition":[240],"maximum":[243],"multiplication":[245],"arithmetic":[247],"addition),":[248],"ordinary":[253],"piecewise":[256],"linear":[257],"functions.":[261],"As":[262],"our":[263],"numerical":[264],"experience":[265],"shows,":[266],"proposed":[268],"converges":[270],"finite":[273],"number":[274],"steps":[276],"provides":[278],"reasonably":[280],"accurate":[281],"solution":[282],"considered.":[286]},"counts_by_year":[],"updated_date":"2025-11-19T23:35:23.961156","created_date":"2025-10-10T00:00:00"}