{"id":"https://openalex.org/W1600918306","doi":"https://doi.org/10.1137/141002062","title":"A Preconditioner for A Primal-Dual Newton Conjugate Gradient Method for Compressed Sensing Problems","display_name":"A Preconditioner for A Primal-Dual Newton Conjugate Gradient Method for Compressed Sensing Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1600918306","doi":"https://doi.org/10.1137/141002062","mag":"1600918306"},"language":"en","primary_location":{"id":"doi:10.1137/141002062","is_oa":true,"landing_page_url":"https://doi.org/10.1137/141002062","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1137/141002062","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035637270","display_name":"Ioannis Dassios","orcid":"https://orcid.org/0000-0001-8763-8741"},"institutions":[{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ioannis Dassios","raw_affiliation_strings":["School of Mathematics and Maxwell Institute, The Univer-sity of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","School of Mathematics and Maxwell Institute, The University of Edin-burgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The Univer-sity of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The University of Edin-burgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050838896","display_name":"Kimon Fountoulakis","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kimon Fountoulakis","raw_affiliation_strings":["School of Mathematics and Maxwell Institute, The University of Edin-burgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","School of Mathematics and Maxwell Institute, The Univer-sity of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The University of Edin-burgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The Univer-sity of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033855320","display_name":"Jacek Gondzio","orcid":"https://orcid.org/0000-0002-6270-4666"},"institutions":[{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jacek Gondzio","raw_affiliation_strings":["School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","School of Mathematics and Maxwell Institute, The Univer-sity of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","School of Mathematics and Maxwell Institute, The University of Edin-burgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The Univer-sity of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Mathematics and Maxwell Institute, The University of Edin-burgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0159,"has_fulltext":true,"cited_by_count":89,"citation_normalized_percentile":{"value":0.92964544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"37","issue":"6","first_page":"A2783","last_page":"A2812"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/preconditioner","display_name":"Preconditioner","score":0.9698560237884521},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8677435517311096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6673139333724976},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.635905385017395},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5176501870155334},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.49247583746910095},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47084948420524597},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.462560772895813},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.46049147844314575},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.4554157257080078},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.43868985772132874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4000627100467682},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.37599486112594604},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3283003866672516},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27147215604782104},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.24617570638656616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20054376125335693},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14062532782554626},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05727273225784302}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9698560237884521},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8677435517311096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6673139333724976},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.635905385017395},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5176501870155334},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.49247583746910095},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47084948420524597},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.462560772895813},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.46049147844314575},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.4554157257080078},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.43868985772132874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4000627100467682},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37599486112594604},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3283003866672516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27147215604782104},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.24617570638656616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20054376125335693},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14062532782554626},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05727273225784302},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/141002062","is_oa":true,"landing_page_url":"https://doi.org/10.1137/141002062","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/280a7ccc-9193-437b-a1c6-38bbfebea627","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11820/280a7ccc-9193-437b-a1c6-38bbfebea627","pdf_url":"https://www.pure.ed.ac.uk/ws/files/21713799/preconditionerCS.pdf","source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.ed.ac.uk:publications/280a7ccc-9193-437b-a1c6-38bbfebea627","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/280a7ccc-9193-437b-a1c6-38bbfebea627","pdf_url":"https://www.pure.ed.ac.uk/ws/files/21713799/preconditionerCS.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dassios, I, Fountoulakis, K & Gondzio, J 2015, 'A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems', SIAM Journal on Scientific Computing, vol. 37, no. 6, pp. A2783-A2812. https://doi.org/10.1137/141002062","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/280a7ccc-9193-437b-a1c6-38bbfebea627","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.11820/280a7ccc-9193-437b-a1c6-38bbfebea627","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dassios, I, Fountoulakis, K & Gondzio, J 2015, 'A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems', SIAM Journal on Scientific Computing, vol. 37, no. 6, pp. A2783-A2812. https://doi.org/10.1137/141002062","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1137/141002062","is_oa":true,"landing_page_url":"https://doi.org/10.1137/141002062","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4804838022","display_name":"Mathematics for Vast Digital Resources","funder_award_id":"EP/I017127/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G680746371","display_name":null,"funder_award_id":"EP/I017127/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1547941176","https://openalex.org/W1953936588","https://openalex.org/W1972010412","https://openalex.org/W1985588167","https://openalex.org/W1986891697","https://openalex.org/W2009702064","https://openalex.org/W2015418199","https://openalex.org/W2023722580","https://openalex.org/W2028349405","https://openalex.org/W2051882509","https://openalex.org/W2054010646","https://openalex.org/W2069912449","https://openalex.org/W2077472656","https://openalex.org/W2103955025","https://openalex.org/W2107604145","https://openalex.org/W2119058682","https://openalex.org/W2122548617","https://openalex.org/W2130120519","https://openalex.org/W2142211803","https://openalex.org/W2164449950","https://openalex.org/W2167732364","https://openalex.org/W3105279496"],"related_works":["https://openalex.org/W2098528027","https://openalex.org/W3159557833","https://openalex.org/W2005717169","https://openalex.org/W2183734858","https://openalex.org/W3159907817","https://openalex.org/W2941778027","https://openalex.org/W4319027779","https://openalex.org/W2388344948","https://openalex.org/W2060532089","https://openalex.org/W4229957265"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"are":[4,20,73],"concerned":[5],"with":[6,84],"the":[7,15,29,80,85],"solution":[8],"of":[9,82],"compressed":[10],"sensing":[11],"(CS)":[12],"problems":[13,77],"where":[14],"signals":[16],"to":[17,54,89],"be":[18],"recovered":[19],"sparse":[21],"in":[22,36],"coherent":[23],"and":[24,43,61],"redundant":[25],"dictionaries.":[26],"We":[27,57],"extend":[28],"primal-dual":[30],"Newton":[31],"Conjugate":[32],"Gradient":[33],"method":[34],"(pdNCG)":[35],"[T.":[37],"F.":[38],"Chan,":[39],"G.":[40],"H.":[41],"Golub,":[42],"P.":[44],"Mulet,":[45],"SIAM":[46],"J.":[47],"Sci.":[48],"Comput.,":[49],"20":[50],"(1999),":[51],"pp.":[52],"1964--1977]":[53],"CS":[55,76],"problems.":[56],"provide":[58],"an":[59],"inexpensive":[60],"provably":[62],"effective":[63],"preconditioning":[64],"technique":[65],"for":[66],"linear":[67],"systems":[68],"using":[69],"pdNCG.":[70],"Numerical":[71],"results":[72],"presented":[74],"on":[75],"which":[78],"demonstrate":[79],"performance":[81],"pdNCG":[83],"proposed":[86],"preconditioner":[87],"compared":[88],"state-of-the-art":[90],"existing":[91],"solvers.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":49},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-30T13:55:48.251075","created_date":"2025-10-10T00:00:00"}