{"id":"https://openalex.org/W134269462","doi":"https://doi.org/10.1515/cmam-2015-0033","title":"Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation","display_name":"Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation","publication_year":2015,"publication_date":"2015-11-26","ids":{"openalex":"https://openalex.org/W134269462","doi":"https://doi.org/10.1515/cmam-2015-0033","mag":"134269462"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2015-0033","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2015-0033","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1408.5224","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043445843","display_name":"Boris N. Khoromskij","orcid":"https://orcid.org/0000-0002-5853-5521"},"institutions":[{"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":"Boris Khoromskij","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22\u201326, 04103 Leipzig, Germany"],"raw_orcid":null,"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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072638484","display_name":"Alexander Veit","orcid":"https://orcid.org/0000-0002-3177-0812"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander Veit","raw_affiliation_strings":["Department of Computer Science, University of Chicago, 1100 East 58th Street, Chicago, IL 60637, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Chicago, 1100 East 58th Street, Chicago, IL 60637, USA","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043445843"],"corresponding_institution_ids":["https://openalex.org/I4210091327"],"apc_list":{"value":2400,"currency":"EUR","value_usd":2712},"apc_paid":null,"fwci":0.6813,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66799205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"1","first_page":"145","last_page":"159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9706000089645386,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6826251745223999},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6032201051712036},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5526102185249329},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5521383285522461},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5469257831573486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5448323488235474},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.4873810410499573},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44861119985580444},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.44394412636756897},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4426971971988678},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4186442196369171},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2819787263870239},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26133185625076294},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24852100014686584},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08991879224777222},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.0749601423740387}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6826251745223999},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6032201051712036},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5526102185249329},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5521383285522461},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5469257831573486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5448323488235474},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.4873810410499573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44861119985580444},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.44394412636756897},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4426971971988678},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4186442196369171},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2819787263870239},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26133185625076294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24852100014686584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08991879224777222},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0749601423740387},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1515/cmam-2015-0033","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2015-0033","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1408.5224","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1408.5224","pdf_url":"https://arxiv.org/pdf/1408.5224","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:134269462","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1408.5224","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.665.4201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.665.4201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.uchicago.edu/%7Eaveit/pdf/HighOscQuad.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:729174","is_oa":false,"landing_page_url":"http://edoc.mpg.de/729174","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":"Computational Methods in Applied Mathematics, v.16, 145-159 (2016)","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1408.5224","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1408.5224","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:arXiv.org:1408.5224","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1408.5224","pdf_url":"https://arxiv.org/pdf/1408.5224","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W134269462.pdf","grobid_xml":"https://content.openalex.org/works/W134269462.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W111373153","https://openalex.org/W2001518794","https://openalex.org/W2024165284","https://openalex.org/W2025267249","https://openalex.org/W2032439996","https://openalex.org/W2033022456","https://openalex.org/W2044380739","https://openalex.org/W2076204025","https://openalex.org/W2081814612","https://openalex.org/W2509236952","https://openalex.org/W2780261029"],"related_works":["https://openalex.org/W2549636337","https://openalex.org/W1745964025","https://openalex.org/W2790362370","https://openalex.org/W3100989705","https://openalex.org/W2119502614","https://openalex.org/W2897844906","https://openalex.org/W2138221991","https://openalex.org/W2744610720","https://openalex.org/W2791336299","https://openalex.org/W1971959006","https://openalex.org/W3116830291","https://openalex.org/W2252252820","https://openalex.org/W2561406503","https://openalex.org/W2281227263","https://openalex.org/W1942523955","https://openalex.org/W2339912509","https://openalex.org/W2389006649","https://openalex.org/W2128243992","https://openalex.org/W2377019927","https://openalex.org/W3010485540"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"propose":[2],"a":[3,11,37,45,65,122],"new":[4],"method":[5,110],"for":[6,44,111,125],"the":[7,19,24,51,70,105,130,140,151,154],"efficient":[8,134],"approximation":[9,55,109,132],"of":[10,13,56,83,114,136,143,153],"class":[12],"highly":[14],"oscillatory":[15,20,84],"weighted":[16],"integrals":[17,85],"where":[18],"function":[21],"depends":[22],"on":[23,50,159],"frequency":[25,146],"parameter":[26],"\u03c9":[27],"\u2265":[28],"0":[29],"${\\omega":[30],"\\ge":[31],"0}$":[32],",":[33],"typically":[34,98],"varying":[35],"in":[36,64,99,117,119,139,162],"large":[38,100],"interval.":[39],"Our":[40],"approach":[41],"is":[42,77],"based,":[43],"fixed":[46],"but":[47],"arbitrary":[48],"oscillator,":[49],"pre-computation":[52],"and":[53,133,145,164],"low-parametric":[54],"certain":[57],"\u03c9-dependent":[58],"prototype":[59,80],"functions":[60,81,138],"whose":[61],"evaluation":[62],"leads":[63],"straightforward":[66],"way":[67],"to":[68,90,95],"recover":[69],"target":[71],"integral.":[72],"The":[73],"difficulty":[74],"that":[75,78],"arises":[76],"these":[79,137],"consist":[82],"which":[86],"makes":[87],"them":[88],"difficult":[89],"evaluate.":[91],"Furthermore,":[92],"they":[93],"have":[94],"be":[96],"approximated":[97],"intervals.":[101],"Here":[102],"we":[103],"use":[104],"quantized-tensor":[106],"train":[107],"(QTT)":[108],"functional":[112],"M-vectors":[113],"logarithmic":[115],"complexity":[116],"M":[118],"combination":[120],"with":[121],"cross-approximation":[123],"scheme":[124,158],"TT":[126],"tensors.":[127],"This":[128],"allows":[129],"accurate":[131],"storage":[135],"wide":[141],"range":[142],"grid":[144],"parameters.":[147],"Numerical":[148],"examples":[149,161],"illustrate":[150],"efficiency":[152],"QTT-based":[155],"numerical":[156],"integration":[157],"various":[160],"one":[163],"several":[165],"spatial":[166],"dimensions.":[167]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
