{"id":"https://openalex.org/W2059875127","doi":"https://doi.org/10.1007/s00607-005-0144-0","title":"Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions","display_name":"Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions","publication_year":2005,"publication_date":"2005-12-05","ids":{"openalex":"https://openalex.org/W2059875127","doi":"https://doi.org/10.1007/s00607-005-0144-0","mag":"2059875127"},"language":"en","primary_location":{"id":"doi:10.1007/s00607-005-0144-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00607-005-0144-0","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084653980","display_name":"Wolfgang Hackbusch","orcid":"https://orcid.org/0000-0002-4801-6189"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"W. Hackbusch","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany","Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany#TAB#","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043445843","display_name":"Boris N. Khoromskij","orcid":"https://orcid.org/0000-0002-5853-5521"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"B. N. Khoromskij","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany","Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103, Leipzig, Germany#TAB#","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084653980"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210091327"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.8297,"has_fulltext":false,"cited_by_count":128,"citation_normalized_percentile":{"value":0.91071429,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"76","issue":"3-4","first_page":"177","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9994999766349792,"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":0.9994999766349792,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9983000159263611,"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/mathematics","display_name":"Mathematics","score":0.8014377355575562},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.785700798034668},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.5884226560592651},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.5556513667106628},{"id":"https://openalex.org/keywords/sinc-function","display_name":"Sinc function","score":0.5503048300743103},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5104169249534607},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.5063649415969849},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5054714679718018},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4658642113208771},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4220184087753296},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4141230285167694},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.39334362745285034},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32109588384628296},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30207252502441406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8014377355575562},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.785700798034668},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.5884226560592651},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.5556513667106628},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.5503048300743103},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5104169249534607},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.5063649415969849},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5054714679718018},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4658642113208771},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4220184087753296},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4141230285167694},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.39334362745285034},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32109588384628296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30207252502441406},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00607-005-0144-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00607-005-0144-0","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.966.9593","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.966.9593","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mis.mpg.de/preprints/2005/preprint2005_30.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:304846","is_oa":false,"landing_page_url":"http://edoc.mpg.de/304846","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"Computing (Wien), v.76, 177-202 (2006)","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W201725292","https://openalex.org/W1510864383","https://openalex.org/W1535160936","https://openalex.org/W1569304948","https://openalex.org/W1597318091","https://openalex.org/W1976016599","https://openalex.org/W1980428773","https://openalex.org/W1995356931","https://openalex.org/W1998665522","https://openalex.org/W2002598080","https://openalex.org/W2009253094","https://openalex.org/W2016075148","https://openalex.org/W2018282388","https://openalex.org/W2018419001","https://openalex.org/W2028247581","https://openalex.org/W2030565709","https://openalex.org/W2035766380","https://openalex.org/W2055721343","https://openalex.org/W2078789945","https://openalex.org/W2079211982","https://openalex.org/W2079407403","https://openalex.org/W2091861914","https://openalex.org/W2122137889","https://openalex.org/W2157005274","https://openalex.org/W2161933414","https://openalex.org/W2500371008","https://openalex.org/W4253999865","https://openalex.org/W4293185733","https://openalex.org/W6630405484"],"related_works":["https://openalex.org/W4298860571","https://openalex.org/W2053693274","https://openalex.org/W4384499925","https://openalex.org/W2108396447","https://openalex.org/W1990641396","https://openalex.org/W3098366737","https://openalex.org/W4237608024","https://openalex.org/W2964330822","https://openalex.org/W4297913686","https://openalex.org/W2059875127"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
