{"id":"https://openalex.org/W1977458753","doi":"https://doi.org/10.1137/070686676","title":"Exact and Approximate Sparse Solutions of Underdetermined Linear Equations","display_name":"Exact and Approximate Sparse Solutions of Underdetermined Linear Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1977458753","doi":"https://doi.org/10.1137/070686676","mag":"1977458753"},"language":"en","primary_location":{"id":"doi:10.1137/070686676","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070686676","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific 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/A5108394769","display_name":"Sadegh Jokar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sadegh Jokar","raw_affiliation_strings":["jokar@math.tu-berlin.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"jokar@math.tu-berlin.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033982876","display_name":"Marc E. Pfetsch","orcid":"https://orcid.org/0000-0002-0947-7193"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc E. Pfetsch","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3929,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.91971413,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"1","first_page":"23","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.8795636892318726},{"id":"https://openalex.org/keywords/underdetermined-system","display_name":"Underdetermined system","score":0.8777387142181396},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6896204948425293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6756904125213623},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.669852614402771},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5842820405960083},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.43954554200172424},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40136948227882385},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.399835467338562},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.1290622055530548},{"id":"https://openalex.org/keywords/matching-pursuit","display_name":"Matching pursuit","score":0.11220133304595947},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06760108470916748}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.8795636892318726},{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.8777387142181396},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6896204948425293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6756904125213623},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.669852614402771},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5842820405960083},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.43954554200172424},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40136948227882385},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.399835467338562},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.1290622055530548},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.11220133304595947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06760108470916748}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070686676","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070686676","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.4770","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.4770","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.matheon.de/preprints/4071_sparse.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.1889","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.1889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.zib.de/Publications/Reports/ZR-07-05.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W130282726","https://openalex.org/W588032555","https://openalex.org/W1963547452","https://openalex.org/W1971697593","https://openalex.org/W1986931325","https://openalex.org/W1989009613","https://openalex.org/W1992155810","https://openalex.org/W2011039300","https://openalex.org/W2028781966","https://openalex.org/W2045491595","https://openalex.org/W2045831651","https://openalex.org/W2050834445","https://openalex.org/W2057427500","https://openalex.org/W2063434077","https://openalex.org/W2075779886","https://openalex.org/W2080815943","https://openalex.org/W2082030917","https://openalex.org/W2086869478","https://openalex.org/W2096185893","https://openalex.org/W2097323375","https://openalex.org/W2099641086","https://openalex.org/W2113369973","https://openalex.org/W2114147096","https://openalex.org/W2116148865","https://openalex.org/W2127271355","https://openalex.org/W2128659236","https://openalex.org/W2129131372","https://openalex.org/W2145096794","https://openalex.org/W2147656689","https://openalex.org/W2149206122","https://openalex.org/W2151693816","https://openalex.org/W2153333938","https://openalex.org/W2154332973","https://openalex.org/W2160396672","https://openalex.org/W2164452299","https://openalex.org/W2167839759","https://openalex.org/W2294690908","https://openalex.org/W2296616510","https://openalex.org/W4250955649","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4297960547","https://openalex.org/W2081047164","https://openalex.org/W2217228542","https://openalex.org/W3177062893","https://openalex.org/W2734989685","https://openalex.org/W3125143773","https://openalex.org/W2007032764","https://openalex.org/W803550684","https://openalex.org/W2483226803","https://openalex.org/W4352977312"],"abstract_inverted_index":{"In":[0],"this":[1,74],"paper,":[2],"we":[3,104],"empirically":[4],"investigate":[5,59],"the":[6,33,46,60,63,82,87,95,98,113,122,126],"NP-hard":[7],"problem":[8,26,50,75],"of":[9,62,81,97],"finding":[10],"sparsest":[11],"solutions":[12,18,54,90],"to":[13,51,93,121,133,138],"linear":[14],"equation":[15],"systems,":[16],"i.e.,":[17],"with":[19],"as":[20,23],"few":[21],"nonzeros":[22],"possible.":[24],"This":[25],"has":[27],"recently":[28],"received":[29],"considerable":[30],"interest":[31],"in":[32,78],"sparse":[34],"approximation":[35],"and":[36,58,135],"signal":[37],"processing":[38],"literature.":[39,83],"We":[40,66],"use":[41],"a":[42,130],"branch-and-cut":[43],"approach":[44],"via":[45],"maximum":[47],"feasible":[48],"subsystem":[49],"compute":[52],"optimal":[53,64,89],"for":[55,73,101],"small":[56,85],"instances":[57,103],"uniqueness":[61],"solutions.":[65],"furthermore":[67],"discuss":[68],"six":[69],"(modifications":[70],"of)":[71],"heuristics":[72,128],"that":[76,112],"appear":[77],"different":[79],"parts":[80],"For":[84],"instances,":[86],"exact":[88],"allow":[91],"us":[92],"evaluate":[94],"quality":[96],"heuristics,":[99],"while":[100],"larger":[102],"compare":[105],"their":[106],"relative":[107],"performance.":[108],"One":[109],"outcome":[110],"is":[111],"so-called":[114],"basis":[115],"pursuit":[116],"heuristic":[117],"performs":[118],"worse,":[119],"compared":[120],"other":[123],"methods.":[124],"Among":[125],"best":[127],"are":[129],"method":[131],"due":[132,137],"Mangasarian":[134],"one":[136],"Chinneck.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
