{"id":"https://openalex.org/W1975742941","doi":"https://doi.org/10.1137/050630982","title":"Integration Preconditioning Matrix for Ultraspherical Pseudospectral Operators","display_name":"Integration Preconditioning Matrix for Ultraspherical Pseudospectral Operators","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1975742941","doi":"https://doi.org/10.1137/050630982","mag":"1975742941"},"language":"en","primary_location":{"id":"doi:10.1137/050630982","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630982","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/A5082683405","display_name":"Elsayed M.E. Elbarbary","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Elsayed M. E. Elbarbary","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5082683405"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.09276488,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"28","issue":"3","first_page":"1186","last_page":"1201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9977999925613403,"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/preconditioner","display_name":"Preconditioner","score":0.8339284062385559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7097412347793579},{"id":"https://openalex.org/keywords/pseudospectral-optimal-control","display_name":"Pseudospectral optimal control","score":0.701820433139801},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.573182225227356},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5324481725692749},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.5249711871147156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49105358123779297},{"id":"https://openalex.org/keywords/chebyshev-pseudospectral-method","display_name":"Chebyshev pseudospectral method","score":0.48920369148254395},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.478786826133728},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.41611388325691223},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3775763213634491},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.09687590599060059},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.09525129199028015},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.0828598141670227}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8339284062385559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7097412347793579},{"id":"https://openalex.org/C154304650","wikidata":"https://www.wikidata.org/wiki/Q7255577","display_name":"Pseudospectral optimal control","level":5,"score":0.701820433139801},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.573182225227356},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5324481725692749},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.5249711871147156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49105358123779297},{"id":"https://openalex.org/C122107654","wikidata":"https://www.wikidata.org/wiki/Q5089017","display_name":"Chebyshev pseudospectral method","level":5,"score":0.48920369148254395},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.478786826133728},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.41611388325691223},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3775763213634491},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.09687590599060059},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.09525129199028015},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.0828598141670227},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050630982","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630982","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W140628048","https://openalex.org/W1540935623","https://openalex.org/W1558279604","https://openalex.org/W1971099220","https://openalex.org/W1973342667","https://openalex.org/W1976538615","https://openalex.org/W1984147483","https://openalex.org/W1985144286","https://openalex.org/W1990038465","https://openalex.org/W1996160600","https://openalex.org/W2002391771","https://openalex.org/W2002952441","https://openalex.org/W2010569986","https://openalex.org/W2019470769","https://openalex.org/W2023988191","https://openalex.org/W2030426577","https://openalex.org/W2036614641","https://openalex.org/W2045111266","https://openalex.org/W2048050098","https://openalex.org/W2051567707","https://openalex.org/W2069736604","https://openalex.org/W2078316951","https://openalex.org/W2084176393","https://openalex.org/W2088537472","https://openalex.org/W2108473871","https://openalex.org/W2131236715","https://openalex.org/W2136431693","https://openalex.org/W2158575547","https://openalex.org/W2297327363","https://openalex.org/W2318788438","https://openalex.org/W2319345516","https://openalex.org/W2801179766","https://openalex.org/W3038165843","https://openalex.org/W4245090284","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W2550657075","https://openalex.org/W2281601070","https://openalex.org/W2761671048","https://openalex.org/W2143234151","https://openalex.org/W2354694671","https://openalex.org/W2029764875","https://openalex.org/W2027623489","https://openalex.org/W2360369146","https://openalex.org/W2192624384","https://openalex.org/W1512809069"],"abstract_inverted_index":{"In":[0,46,56],"this":[1],"paper,":[2],"we":[3,50,60],"give":[4],"an":[5,15,52],"integration":[6,53],"rectangular":[7,54],"preconditioner":[8],"for":[9],"ultraspherical":[10],"pseudospectral":[11,27],"operators.":[12],"We":[13],"present":[14],"explicit":[16],"solution":[17],"of":[18,29,38],"matrix":[19,76],"equations":[20],"with":[21],"the":[22,26,30,47,57,67,71,74],"structure":[23],"provided":[24],"by":[25],"discretization":[28],"nth-order":[31],"differential":[32],"operator,":[33],"subject":[34],"to":[35,65],"various":[36],"types":[37],"boundary":[39,68],"conditions.":[40],"This":[41],"occurs":[42],"in":[43],"two":[44],"steps.":[45],"first":[48],"step":[49,59],"introduce":[51],"preconditioner.":[55],"second":[58],"use":[61],"a":[62,78],"new":[63],"strategy":[64],"impose":[66],"conditions,":[69],"on":[70],"condition":[72],"that":[73],"coefficients":[75],"has":[77],"known":[79],"inverse.":[80],"Computational":[81],"examples":[82],"are":[83],"given.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
