{"id":"https://openalex.org/W7140636904","doi":"https://doi.org/10.48550/arxiv.2603.23858","title":"Stable High-Order Interpolation on the Grassmann Manifold by Maximum-Volume Coordinates and Arnoldi Orthogonalization","display_name":"Stable High-Order Interpolation on the Grassmann Manifold by Maximum-Volume Coordinates and Arnoldi Orthogonalization","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140636904","doi":"https://doi.org/10.48550/arxiv.2603.23858"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.23858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2603.23858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130646978","display_name":"Qiang Niu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Niu, Qiang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130707370","display_name":"Wen Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Wen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130719278","display_name":"Jie Fei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fei, Jie","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130648009","display_name":"Ruoyu Xiong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiong, Ruoyu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130674961","display_name":"Yuxuan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yuxuan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5130646978"],"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/T10514","display_name":"Numerical methods in engineering","score":0.567799985408783,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.567799985408783,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.25270000100135803,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.02070000022649765,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.7391999959945679},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.597100019454956},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5583000183105469},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.47600001096725464},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.4733000099658966},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.4713999927043915},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.4620000123977661},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4546000063419342},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4499000012874603},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.4456999897956848}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7534000277519226},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.7391999959945679},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.597100019454956},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5583000183105469},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.47600001096725464},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.4733000099658966},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.4620000123977661},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.4456999897956848},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C205280321","wikidata":"https://www.wikidata.org/wiki/Q3800523","display_name":"Birkhoff interpolation","level":5,"score":0.4163999855518341},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40220001339912415},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3662000000476837},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.3458000123500824},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.3228999972343445},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.32249999046325684},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3095000088214874},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.2939999997615814},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.2831999957561493},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.28130000829696655},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.2800000011920929},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C74349738","wikidata":"https://www.wikidata.org/wiki/Q1517914","display_name":"Closed manifold","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25440001487731934},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.23858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.23858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"High-order":[0],"interpolation":[1,79],"on":[2],"the":[3,12,24,57,68,73,96,99,113,116,120,128],"Grassmann":[4],"manifold":[5,42],"$\\Gr(n,":[6],"p)$":[7],"is":[8,105],"often":[9],"hindered":[10],"by":[11],"computational":[13],"overhead":[14],"and":[15,80,119],"derivative":[16],"instability":[17],"of":[18,101,115],"SVD-based":[19],"geometric":[20,117],"mappings.":[21],"To":[22],"solve":[23],"challenges,":[25],"we":[26,71],"propose":[27],"a":[28,47],"stabilized":[29],"framework":[30,131],"that":[31,127],"combines":[32],"Maximum-Volume":[33],"(MV)":[34],"local":[35],"coordinates":[36],"with":[37],"Arnoldi-orthogonalized":[38],"polynomial":[39,121,139],"bases.":[40],"First,":[41],"data":[43],"are":[44,109],"mapped":[45],"to":[46,62,111],"well-conditioned":[48],"Euclidean":[49],"domain":[50],"via":[51],"MV":[52],"coordinates.":[53,66],"The":[54],"approach":[55],"bypasses":[56],"costly":[58],"matrix":[59],"factorizations":[60],"inherent":[61],"traditional":[63],"Riemannian":[64],"normal":[65],"Within":[67],"coordinate":[69],"space,":[70],"use":[72],"Vandermonde-with-Arnoldi":[74],"(V+A)":[75],"method":[76],"for":[77,85],"Lagrange":[78],"its":[81],"confluent":[82],"extension":[83],"(CV+A)":[84],"derivative-enriched":[86],"Hermite":[87],"interpolation.":[88,140],"By":[89],"constructing":[90],"discrete":[91],"orthogonal":[92],"bases":[93],"directly":[94],"from":[95],"parameter":[97],"nodes,":[98],"solution":[100],"ill-conditioned":[102],"linear":[103],"system":[104],"avoided.":[106],"Theoretical":[107],"bounds":[108],"established":[110],"verify":[112],"stability":[114],"mapping":[118],"approximation.":[122],"Extensive":[123],"numerical":[124],"experiments":[125],"demonstrate":[126],"proposed":[129],"MV-(C)V+A":[130],"can":[132],"produce":[133],"highly":[134],"accurate":[135],"approximation":[136],"in":[137],"high-degree":[138]},"counts_by_year":[],"updated_date":"2026-03-27T06:05:27.210665","created_date":"2026-03-27T00:00:00"}
