{"id":"https://openalex.org/W4211094263","doi":"https://doi.org/10.1017/s0962492915000021","title":"Preconditioning","display_name":"Preconditioning","publication_year":2015,"publication_date":"2015-04-27","ids":{"openalex":"https://openalex.org/W4211094263","doi":"https://doi.org/10.1017/s0962492915000021"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492915000021","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492915000021","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","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/A5014826552","display_name":"Andy Wathen","orcid":"https://orcid.org/0000-0001-9992-5588"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"A. J. Wathen","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK E-mail:","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014826552"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":16.7184,"has_fulltext":false,"cited_by_count":202,"citation_normalized_percentile":{"value":0.99403491,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"24","issue":null,"first_page":"329","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.742830216884613},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.563665509223938},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5256258845329285},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4603464603424072},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.44856497645378113},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40220844745635986},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30189943313598633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18782782554626465},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05970662832260132}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.742830216884613},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.563665509223938},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5256258845329285},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4603464603424072},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.44856497645378113},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40220844745635986},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30189943313598633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18782782554626465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05970662832260132},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0962492915000021","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492915000021","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1294628090","display_name":null,"funder_award_id":"EP/I01893X/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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":161,"referenced_works":["https://openalex.org/W4509327","https://openalex.org/W149522324","https://openalex.org/W274121196","https://openalex.org/W648869842","https://openalex.org/W649715400","https://openalex.org/W654805605","https://openalex.org/W1425400007","https://openalex.org/W1492771151","https://openalex.org/W1502854356","https://openalex.org/W1506342804","https://openalex.org/W1511121222","https://openalex.org/W1512732958","https://openalex.org/W1519509134","https://openalex.org/W1524137286","https://openalex.org/W1530661923","https://openalex.org/W1533471646","https://openalex.org/W1542243431","https://openalex.org/W1607836799","https://openalex.org/W1887595486","https://openalex.org/W1916091028","https://openalex.org/W1969098340","https://openalex.org/W1970009422","https://openalex.org/W1972148882","https://openalex.org/W1973709085","https://openalex.org/W1973836629","https://openalex.org/W1975714268","https://openalex.org/W1976685335","https://openalex.org/W1977444623","https://openalex.org/W1980053021","https://openalex.org/W1980431326","https://openalex.org/W1981220107","https://openalex.org/W1981883552","https://openalex.org/W1981908221","https://openalex.org/W1984797906","https://openalex.org/W1986225835","https://openalex.org/W1986652366","https://openalex.org/W1987152170","https://openalex.org/W1994794997","https://openalex.org/W1994805693","https://openalex.org/W1997181819","https://openalex.org/W1997831216","https://openalex.org/W2000582360","https://openalex.org/W2002102128","https://openalex.org/W2005040897","https://openalex.org/W2005047411","https://openalex.org/W2006910694","https://openalex.org/W2007894711","https://openalex.org/W2008848819","https://openalex.org/W2011936333","https://openalex.org/W2017085690","https://openalex.org/W2018419001","https://openalex.org/W2018850201","https://openalex.org/W2020207843","https://openalex.org/W2022396725","https://openalex.org/W2022397154","https://openalex.org/W2022665438","https://openalex.org/W2022819055","https://openalex.org/W2022852340","https://openalex.org/W2024381649","https://openalex.org/W2025836747","https://openalex.org/W2027162534","https://openalex.org/W2029087005","https://openalex.org/W2032599937","https://openalex.org/W2033986961","https://openalex.org/W2038516134","https://openalex.org/W2039789965","https://openalex.org/W2041660628","https://openalex.org/W2041876368","https://openalex.org/W2042199958","https://openalex.org/W2046064079","https://openalex.org/W2049644675","https://openalex.org/W2050206349","https://openalex.org/W2051133095","https://openalex.org/W2051185579","https://openalex.org/W2051917325","https://openalex.org/W2053050827","https://openalex.org/W2053315218","https://openalex.org/W2053893326","https://openalex.org/W2055116131","https://openalex.org/W2059610447","https://openalex.org/W2060675257","https://openalex.org/W2061171222","https://openalex.org/W2062618120","https://openalex.org/W2065385312","https://openalex.org/W2066308409","https://openalex.org/W2066531315","https://openalex.org/W2067313886","https://openalex.org/W2069601896","https://openalex.org/W2070419067","https://openalex.org/W2070448527","https://openalex.org/W2072118131","https://openalex.org/W2073753111","https://openalex.org/W2074780612","https://openalex.org/W2075237894","https://openalex.org/W2077791079","https://openalex.org/W2078692435","https://openalex.org/W2078843646","https://openalex.org/W2079308547","https://openalex.org/W2081523040","https://openalex.org/W2082001547","https://openalex.org/W2082606496","https://openalex.org/W2083206954","https://openalex.org/W2085259167","https://openalex.org/W2085581918","https://openalex.org/W2089099677","https://openalex.org/W2093753671","https://openalex.org/W2097897435","https://openalex.org/W2098102734","https://openalex.org/W2099359799","https://openalex.org/W2100481637","https://openalex.org/W2100720421","https://openalex.org/W2111268954","https://openalex.org/W2114583457","https://openalex.org/W2115272362","https://openalex.org/W2117221287","https://openalex.org/W2118431207","https://openalex.org/W2119121660","https://openalex.org/W2121613024","https://openalex.org/W2122137889","https://openalex.org/W2123963295","https://openalex.org/W2126036157","https://openalex.org/W2126042051","https://openalex.org/W2127190985","https://openalex.org/W2130641059","https://openalex.org/W2133248904","https://openalex.org/W2134572726","https://openalex.org/W2136722618","https://openalex.org/W2136750362","https://openalex.org/W2137512990","https://openalex.org/W2140153041","https://openalex.org/W2143228255","https://openalex.org/W2147705138","https://openalex.org/W2148033377","https://openalex.org/W2151317657","https://openalex.org/W2151478420","https://openalex.org/W2152968637","https://openalex.org/W2155216327","https://openalex.org/W2157059822","https://openalex.org/W2162221417","https://openalex.org/W2163715525","https://openalex.org/W2168224303","https://openalex.org/W2170286633","https://openalex.org/W2246376430","https://openalex.org/W2316564661","https://openalex.org/W2750531793","https://openalex.org/W3103404537","https://openalex.org/W3104165448","https://openalex.org/W3135067840","https://openalex.org/W3147515309","https://openalex.org/W4205624883","https://openalex.org/W4231405723","https://openalex.org/W4242964124","https://openalex.org/W4247600657","https://openalex.org/W4300666158","https://openalex.org/W4302564868","https://openalex.org/W6631735221","https://openalex.org/W6658621071","https://openalex.org/W6679086787","https://openalex.org/W6682692198","https://openalex.org/W6743427859","https://openalex.org/W6829195247"],"related_works":["https://openalex.org/W2357256365","https://openalex.org/W2348502264","https://openalex.org/W2365486383","https://openalex.org/W2362059367","https://openalex.org/W2350084742","https://openalex.org/W2901443725","https://openalex.org/W2138831083","https://openalex.org/W2770381769","https://openalex.org/W3184983074","https://openalex.org/W2021940933"],"abstract_inverted_index":{"The":[0],"computational":[1],"solution":[2,12,33],"of":[3,11,17,34,47],"problems":[4],"can":[5],"be":[6],"restricted":[7],"by":[8],"the":[9,27,32,38],"availability":[10],"methods":[13],"for":[14],"linear(ized)":[15],"systems":[16,36],"equations.":[18],"In":[19],"conjunction":[20],"with":[21],"iterative":[22],"methods,":[23],"preconditioning":[24,48],"is":[25,40],"often":[26],"vital":[28],"component":[29],"in":[30],"enabling":[31],"such":[35],"when":[37],"dimension":[39],"large.":[41],"We":[42],"attempt":[43],"a":[44],"broad":[45],"review":[46],"methods.":[49]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":19},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":6}],"updated_date":"2026-06-14T07:44:22.658603","created_date":"2022-02-13T00:00:00"}
