{"id":"https://openalex.org/W7165759444","doi":"https://doi.org/10.48550/arxiv.2606.24423","title":"A sparse spectral method on a class of domains bounded by planar algebraic curves","display_name":"A sparse spectral method on a class of domains bounded by planar algebraic curves","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165759444","doi":"https://doi.org/10.48550/arxiv.2606.24423"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.24423","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24423","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":null,"license_id":null,"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.2606.24423","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109028401","display_name":"Jiajie Yao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yao, Jiajie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019076995","display_name":"Marco Fasondini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fasondini, Marco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010027385","display_name":"Sheehan Olver","orcid":"https://orcid.org/0000-0001-6920-0826"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olver, Sheehan","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/T11435","display_name":"Polynomial and algebraic computation","score":0.36489999294281006,"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":0.36489999294281006,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.15129999816417694,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.10480000078678131,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5353999733924866},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.5286999940872192},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5253000259399414},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4284000098705292},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41290000081062317},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.40290001034736633},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.3882000148296356},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.38370001316070557},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3725999891757965},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.36390000581741333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8636000156402588},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5353999733924866},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5286999940872192},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5253000259399414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43549999594688416},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4284000098705292},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.38370001316070557},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3822000026702881},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.35989999771118164},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3449000120162964},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2786000072956085},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2782000005245209},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.2718999981880188},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.26669999957084656},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.2651999890804291},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.258899986743927},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.25760000944137573},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.25540000200271606}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.24423","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24423","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.24423","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24423","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,139],"develop":[1,99],"a":[2,12,31,105,122],"sparse":[3,92],"spectral":[4,117],"method":[5,23,118],"for":[6,143],"solving":[7],"partial":[8,85],"differential":[9,86],"equations":[10,87],"on":[11,104,127],"class":[13],"of":[14,43,53,78,114,124],"two-dimensional":[15],"geometries":[16,128,144],"bounded":[17],"by":[18],"algebraic":[19,141],"curves.":[20],"The":[21,46,110],"numerical":[22,95,125],"uses":[24],"generalised":[25],"bivariate":[26],"Koornwinder":[27],"polynomials":[28,47,57],"which":[29,37,147],"form":[30],"complete":[32],"orthogonal":[33,56],"basis,":[34],"but":[35],"one":[36],"is":[38,157],"not":[39],"graded":[40],"in":[41,75],"terms":[42],"polynomial":[44],"degree.":[45],"are":[48,69,91,119,131],"built":[49],"from":[50,102],"new":[51],"families":[52],"univariate":[54],"semiclassical":[55],"whose":[58,129],"associated":[59],"operator":[60],"matrices":[61,65,90],"(Jacobi":[62],"matrices,":[63],"raising":[64],"and":[66,112,133],"differentiation":[67],"matrices)":[68],"computed":[70],"with":[71,145],"optimal":[72],"linear":[73],"complexity":[74],"the":[76,88,115,155],"number":[77],"basis":[79],"functions.":[80],"When":[81],"used":[82],"to":[83,107,149],"discretise":[84],"resulting":[89,116],"enabling":[93],"efficient":[94],"solution.":[96],"Moreover,":[97],"we":[98],"fast":[100,151],"transforms":[101],"values":[103],"grid":[106],"expansion":[108],"coefficients.":[109],"efficiency":[111],"accuracy":[113],"illustrated":[120],"through":[121],"series":[123],"experiments":[126],"boundaries":[130],"smooth":[132,135],"piecewise":[134],"including":[136],"non-convex":[137],"geometries.":[138],"observe":[140],"convergence":[142,153],"corners,":[146],"accelerates":[148],"exponentially":[150],"(spectral)":[152],"when":[154],"boundary":[156],"smooth.":[158]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-25T00:00:00"}