{"id":"https://openalex.org/W4414684724","doi":"https://doi.org/10.1137/25m1770965","title":"Krylov and Core Transformation Algorithms for an Inverse Eigenvalue Problem to Compute Recurrences of Multiple Orthogonal Polynomials","display_name":"Krylov and Core Transformation Algorithms for an Inverse Eigenvalue Problem to Compute Recurrences of Multiple Orthogonal Polynomials","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W4414684724","doi":"https://doi.org/10.1137/25m1770965"},"language":"en","primary_location":{"id":"doi:10.1137/25m1770965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1770965","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/20.500.12942/772041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016438928","display_name":"Amin Faghih","orcid":"https://orcid.org/0000-0001-5253-4977"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Amin Faghih","raw_affiliation_strings":["Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090990730","display_name":"Michele Rinelli","orcid":"https://orcid.org/0000-0003-2405-7442"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Michele Rinelli","raw_affiliation_strings":["Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052654029","display_name":"Marc Van Barel","orcid":"https://orcid.org/0000-0002-7372-382X"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Marc Van Barel","raw_affiliation_strings":["Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-7372-382X","affiliations":[{"raw_affiliation_string":"Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039999347","display_name":"Raf Vandebril","orcid":"https://orcid.org/0000-0003-2119-8696"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Raf Vandebril","raw_affiliation_strings":["Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5119789580","display_name":"Robbe Vermeiren","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Robbe Vermeiren","raw_affiliation_strings":["Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium"],"raw_orcid":"https://orcid.org/0009-0006-7008-3675","affiliations":[{"raw_affiliation_string":"Numerical Analysis and Applied Mathematics (NUMA) Unit, Department of Computer Science, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03182083,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"4","first_page":"1190","last_page":"1216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9868000149726868,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9868000149726868,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9203000068664551,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/biorthogonal-system","display_name":"Biorthogonal system","score":0.7651000022888184},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.670799970626831},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.567799985408783},{"id":"https://openalex.org/keywords/orthogonal-transformation","display_name":"Orthogonal transformation","score":0.5633999705314636},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.532800018787384},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.5041999816894531},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5006999969482422},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4043999910354614},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.3978999853134155},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.3959999978542328},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.39489999413490295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7795000076293945},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.7651000022888184},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.670799970626831},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5985999703407288},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.567799985408783},{"id":"https://openalex.org/C54940322","wikidata":"https://www.wikidata.org/wiki/Q3997740","display_name":"Orthogonal transformation","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.532800018787384},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.5041999816894531},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5006999969482422},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.39489999413490295},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.38429999351501465},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3747999966144562},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.3718000054359436},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.36649999022483826},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3605000078678131},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.35040000081062317},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3490999937057495},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.34779998660087585},{"id":"https://openalex.org/C117586675","wikidata":"https://www.wikidata.org/wiki/Q7298489","display_name":"Rayleigh quotient iteration","level":4,"score":0.3278999924659729},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.3273000121116638},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.32269999384880066},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.2872999906539917},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.27399998903274536},{"id":"https://openalex.org/C61987429","wikidata":"https://www.wikidata.org/wiki/Q3064355","display_name":"M-matrix","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.26649999618530273},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.2628999948501587},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/25m1770965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1770965","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/772041","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/772041","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"arXiv","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:arXiv.org:2506.19796","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.19796","pdf_url":"https://arxiv.org/pdf/2506.19796","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2506.19796","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2506.19796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.19796","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":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/772041","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/772041","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"arXiv","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1771928520","display_name":null,"funder_award_id":"12A1325N","funder_id":"https://openalex.org/F4320321587","funder_display_name":"Vlaamse Overheid"},{"id":"https://openalex.org/G39774290","display_name":null,"funder_award_id":"G0A9923N","funder_id":"https://openalex.org/F4320321587","funder_display_name":"Vlaamse Overheid"},{"id":"https://openalex.org/G7519992166","display_name":null,"funder_award_id":"G0B0123N","funder_id":"https://openalex.org/F4320321587","funder_display_name":"Vlaamse Overheid"},{"id":"https://openalex.org/G8104518077","display_name":null,"funder_award_id":"C16/21/002","funder_id":"https://openalex.org/F4320322681","funder_display_name":"Onderzoeksraad, KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320321587","display_name":"Vlaamse Overheid","ror":"https://ror.org/04qxsrb28"},{"id":"https://openalex.org/F4320322681","display_name":"Onderzoeksraad, KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"paper,":[3],"we":[4],"develop":[5],"algorithms":[6,96],"for":[7],"computing":[8],"the":[9,18,22,42,47,64,80,85,90,95,101],"recurrence":[10,86],"coefficients":[11],"corresponding":[12],"to":[13,78,107],"multiple":[14,61],"orthogonal":[15],"polynomials":[16],"on":[17,46,74,100,115],"step-line.":[19],"We":[20,38,88],"reformulate":[21],"problem":[23],"as":[24,112,114],"an":[25],"inverse":[26,103],"eigenvalue":[27,104],"problem,":[28],"which":[29],"can":[30],"be":[31],"solved":[32],"using":[33],"numerical":[34,98],"linear":[35],"algebra":[36],"techniques.":[37],"consider":[39],"two":[40],"approaches:":[41],"first":[43],"is":[44],"based":[45],"link":[48],"with":[49,60,97],"block":[50],"Krylov":[51],"subspaces":[52],"and":[53,92,109],"results":[54],"in":[55],"a":[56,69,75],"biorthogonal":[57],"Lanczos":[58],"process":[59],"starting":[62],"vectors;":[63],"second":[65],"consists":[66],"of":[67,71,94],"applying":[68],"sequence":[70],"Gaussian":[72],"eliminations":[73],"diagonal":[76],"matrix":[77,83],"construct":[79],"banded":[81],"Hessenberg":[82],"containing":[84],"coefficients.":[87],"analyze":[89],"accuracy":[91],"stability":[93],"experiments":[99],"ill-conditioned":[102],"problems":[105],"related":[106],"Kravchuk":[108],"Hahn":[110],"polynomials,":[111],"well":[113],"other":[116],"better":[117],"conditioned":[118],"examples.":[119]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}