{"id":"https://openalex.org/W2061808582","doi":"https://doi.org/10.2478/cmam-2010-0023","title":"Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs","display_name":"Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2061808582","doi":"https://doi.org/10.2478/cmam-2010-0023","mag":"2061808582"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2010-0023","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0023","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0023/pdf","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0023/pdf","any_repository_has_fulltext":false},"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":"B.N. Khoromskij","raw_affiliation_strings":["1Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22-26, D-04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"1Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Inselstr. 22-26, D-04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004111307","display_name":"Ivan Oseledets","orcid":"https://orcid.org/0000-0003-2071-2163"},"institutions":[{"id":"https://openalex.org/I119694697","display_name":"Gubkin Russian State University of Oil and Gas","ror":"https://ror.org/0082yr561","country_code":"RU","type":"education","lineage":["https://openalex.org/I119694697"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"I. Oseledets","raw_affiliation_strings":["2INM RAS, Gubkina str. 8, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"2INM RAS, Gubkina str. 8, Moscow, Russia","institution_ids":["https://openalex.org/I119694697"]}]}],"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":null,"apc_paid":null,"fwci":3.0858,"has_fulltext":true,"cited_by_count":65,"citation_normalized_percentile":{"value":0.90441176,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"4","first_page":"376","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962000250816345,"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/mathematics","display_name":"Mathematics","score":0.8075109124183655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6243796348571777},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5458195805549622},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5404471158981323},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4684709906578064},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4662690758705139},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4294646680355072},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4253518283367157},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.4217474162578583},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2995452284812927},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.27469250559806824},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1197509765625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09042507410049438}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8075109124183655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6243796348571777},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5458195805549622},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5404471158981323},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4684709906578064},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4662690758705139},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4294646680355072},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4253518283367157},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.4217474162578583},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2995452284812927},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.27469250559806824},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1197509765625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09042507410049438},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/cmam-2010-0023","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0023","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0023/pdf","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.636.8401","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.636.8401","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/2010/preprint2010_37.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:542206","is_oa":false,"landing_page_url":"http://edoc.mpg.de/542206","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.10, 376-394 (2010)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/cmam-2010-0023","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0023","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0023/pdf","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320327897","display_name":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften","ror":"https://ror.org/00ez2he07"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2061808582.pdf","grobid_xml":"https://content.openalex.org/works/W2061808582.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W7264485","https://openalex.org/W610236418","https://openalex.org/W1515678755","https://openalex.org/W1967859589","https://openalex.org/W1983156129","https://openalex.org/W1985681033","https://openalex.org/W1989786408","https://openalex.org/W1995406764","https://openalex.org/W2020320699","https://openalex.org/W2024165284","https://openalex.org/W2036604884","https://openalex.org/W2049222546","https://openalex.org/W2055460625","https://openalex.org/W2064332562","https://openalex.org/W2073469810","https://openalex.org/W2084617396","https://openalex.org/W2108138101","https://openalex.org/W2110090002","https://openalex.org/W2116514123","https://openalex.org/W2132267493","https://openalex.org/W2135329423","https://openalex.org/W2163299986","https://openalex.org/W2181856925","https://openalex.org/W2496219407","https://openalex.org/W2738689307","https://openalex.org/W3173412020","https://openalex.org/W4256580027","https://openalex.org/W4285719527","https://openalex.org/W6613143285"],"related_works":["https://openalex.org/W2357336958","https://openalex.org/W4281839678","https://openalex.org/W2535797495","https://openalex.org/W152950973","https://openalex.org/W2300963337","https://openalex.org/W2283235658","https://openalex.org/W3162287216","https://openalex.org/W2108077990","https://openalex.org/W2058487055","https://openalex.org/W2025305727"],"abstract_inverted_index":{"Abstract":[0],"We":[1,63,112],"investigate":[2],"the":[3,7,42,58,66,74,81,85,91,105,108,118,139,146],"convergence":[4],"rate":[5],"of":[6,17,34,47,68,80,90,107,120,148],"quantics-TT":[8],"(QTT)":[9],"stochas-":[10],"tic":[11],"collocation":[12],"tensor":[13],"approximations":[14],"to":[15],"solutions":[16,106],"multiparametric":[18],"elliptic":[19,48],"PDEs":[20,37,49],"and":[21,70,131],"construct":[22],"efficient":[23],"iterative":[24],"methods":[25],"for":[26,39,55,84,104],"solving":[27],"arising":[28],"high-dimensional":[29],"parameter-":[30],"dependent":[31],"algebraic":[32],"systems":[33],"equations.":[35],"Such":[36],"arise,":[38],"example,":[40,56],"in":[41,88,102,128,145],"para-":[43],"metric,":[44],"deterministic":[45],"reformulation":[46],"with":[50],"random":[51],"field":[52],"inputs,":[53],"based,":[54],"on":[57,73,117],"M-term":[59],"truncated":[60],"Karhunen-Lo\u00e8ve":[61],"expansion.":[62],"consider":[64],"both":[65,129],"case":[67],"additive":[69,130],"log-additive":[71,132],"dependence":[72],"multivariate":[75],"parameter.":[76],"The":[77],"local-global":[78],"versions":[79],"QTT-rank":[82],"estimates":[83],"system":[86],"matrix":[87],"terms":[89],"parameter":[92],"space":[93,150],"dimension":[94,147],"is":[95],"proven.":[96],"Similar":[97],"rank":[98],"bounds":[99],"are":[100],"observed":[101],"numerics":[103],"discrete":[109],"linear":[110],"system.":[111],"propose":[113],"QTT-truncated":[114],"iteration":[115],"based":[116],"construction":[119],"solution-adaptive":[121],"preconditioner":[122],"that":[123,138],"provides":[124],"robust":[125],"conver-":[126],"gence":[127],"cases.":[133],"Various":[134],"numerical":[135,140],"tests":[136],"indicate":[137],"complexity":[141],"scales":[142],"almost":[143],"linearly":[144],"parametric":[149],"M.":[151]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}