{"id":"https://openalex.org/W2810372754","doi":"https://doi.org/10.1137/20m132571x","title":"Sparse Compression of Expected Solution Operators","display_name":"Sparse Compression of Expected Solution Operators","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2810372754","doi":"https://doi.org/10.1137/20m132571x","mag":"2810372754"},"language":"en","primary_location":{"id":"doi:10.1137/20m132571x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m132571x","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1807.01741","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035803720","display_name":"Michael Feischl","orcid":"https://orcid.org/0000-0001-7206-1652"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Feischl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014228488","display_name":"Daniel Peterseim","orcid":"https://orcid.org/0000-0001-7213-556X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Peterseim","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035803720"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2887,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.5956452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"6","first_page":"3144","last_page":"3164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/sparse-approximation","display_name":"Sparse approximation","score":0.5864710211753845},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5813379287719727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5604338049888611},{"id":"https://openalex.org/keywords/semi-elliptic-operator","display_name":"Semi-elliptic operator","score":0.5195087194442749},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.5147342681884766},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.5146046876907349},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5114054083824158},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.5030912756919861},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.46912527084350586},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4388889968395233},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.4225146472454071},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.310011625289917},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2976621389389038},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2761019468307495},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.26836055517196655},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21988454461097717},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.18861454725265503}],"concepts":[{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.5864710211753845},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5813379287719727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5604338049888611},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.5195087194442749},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.5147342681884766},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.5146046876907349},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5114054083824158},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.5030912756919861},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.46912527084350586},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4388889968395233},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.4225146472454071},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.310011625289917},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2976621389389038},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2761019468307495},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.26836055517196655},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21988454461097717},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.18861454725265503},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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":7,"locations":[{"id":"doi:10.1137/20m132571x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m132571x","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:EVASTAR-Karlsruhe.de:1000086887","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000086887","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 2365-662X","raw_type":"doc-type:report"},{"id":"pmh:oai:arXiv.org:1807.01741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.01741","pdf_url":"https://arxiv.org/pdf/1807.01741","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2810372754","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1807.01741","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:83360","is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-833600","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"doi:10.48550/arxiv.1807.01741","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1807.01741","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.5445/ir/1000086887","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000086887","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"report"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.01741","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.01741","pdf_url":"https://arxiv.org/pdf/1807.01741","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3587333238","display_name":null,"funder_award_id":"CRC 1173","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4636375529","display_name":null,"funder_award_id":"PE2143/2-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6743243744","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321692","display_name":"Erwin Schr\u00f6dinger International Institute for Mathematics and Physics","ror":"https://ror.org/03prydq77"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1436589512","https://openalex.org/W1506342804","https://openalex.org/W1595193945","https://openalex.org/W1630018803","https://openalex.org/W1965549324","https://openalex.org/W1980404981","https://openalex.org/W1983122553","https://openalex.org/W2014551121","https://openalex.org/W2017085690","https://openalex.org/W2065713338","https://openalex.org/W2099947844","https://openalex.org/W2132400089","https://openalex.org/W2151177334","https://openalex.org/W2153127767","https://openalex.org/W2154003217","https://openalex.org/W2163715525","https://openalex.org/W2263908415","https://openalex.org/W2265795078","https://openalex.org/W2326205531","https://openalex.org/W2465076683","https://openalex.org/W2513676926","https://openalex.org/W2559327389","https://openalex.org/W2594657990","https://openalex.org/W2623463482","https://openalex.org/W2624297319","https://openalex.org/W2799113196","https://openalex.org/W2962840746","https://openalex.org/W2962849402","https://openalex.org/W2963062618","https://openalex.org/W2963244551","https://openalex.org/W2963634130","https://openalex.org/W2963691989","https://openalex.org/W2963707073","https://openalex.org/W2963873422","https://openalex.org/W2963961138","https://openalex.org/W2963977985","https://openalex.org/W2964191339","https://openalex.org/W2970164183","https://openalex.org/W3102723444","https://openalex.org/W3134737121","https://openalex.org/W3193014788","https://openalex.org/W3194996585"],"related_works":["https://openalex.org/W2963634130","https://openalex.org/W2513676926","https://openalex.org/W1980404981","https://openalex.org/W1978447901","https://openalex.org/W1964974227","https://openalex.org/W2150265707","https://openalex.org/W2045355467","https://openalex.org/W2018522516","https://openalex.org/W2891590611","https://openalex.org/W1851272560","https://openalex.org/W2604140356","https://openalex.org/W2770711090","https://openalex.org/W3161805984","https://openalex.org/W2364662824","https://openalex.org/W2946173218","https://openalex.org/W2153700325","https://openalex.org/W2280506408","https://openalex.org/W3137611772","https://openalex.org/W2972990939","https://openalex.org/W2340835927"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,38],"the":[3,35,41,46,81,96],"expected":[4,61,97],"solution":[5,36,62,98],"operator":[6,48,63],"of":[7,34,45,69,95],"prototypical":[8],"linear":[9],"elliptic":[10],"PDEs":[11],"with":[12,75],"random":[13,29,47],"coefficients":[14],"is":[15,25],"well":[16,54],"approximated":[17],"by":[18],"a":[19,28,76,92],"computable":[20],"sparse":[21,42,93],"matrix.":[22],"This":[23],"result":[24],"based":[26],"on":[27],"localized":[30],"orthogonal":[31],"multiresolution":[32],"decomposition":[33],"space":[37],"allows":[39],"both":[40],"approximate":[43,60],"inversion":[44],"represented":[49],"in":[50,67],"this":[51,83],"basis":[52],"as":[53,55],"its":[56],"stochastic":[57],"averaging.":[58],"The":[59],"can":[64],"be":[65],"interpreted":[66],"terms":[68],"classical":[70],"Haar":[71],"wavelets.":[72],"When":[73],"combined":[74],"suitable":[77],"sampling":[78],"approach":[79],"for":[80,90],"expectation,":[82],"construction":[84],"leads":[85],"to":[86],"an":[87],"efficient":[88],"method":[89],"computing":[91],"representation":[94],"operator.":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
