{"id":"https://openalex.org/W2001816900","doi":"https://doi.org/10.1137/0916073","title":"Accuracy and Speed in Computing the Chebyshev Collocation Derivative","display_name":"Accuracy and Speed in Computing the Chebyshev Collocation Derivative","publication_year":1995,"publication_date":"1995-11-01","ids":{"openalex":"https://openalex.org/W2001816900","doi":"https://doi.org/10.1137/0916073","mag":"2001816900"},"language":"en","primary_location":{"id":"doi:10.1137/0916073","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0916073","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":true,"oa_status":"green","oa_url":"https://ntrs.nasa.gov/api/citations/19920003815/downloads/19920003815.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087840965","display_name":"Wai Sun Don","orcid":"https://orcid.org/0009-0005-9531-281X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wai Sun Don","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067334137","display_name":"Alex Solomonoff","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alex Solomonoff","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087840965"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2104,"has_fulltext":true,"cited_by_count":176,"citation_normalized_percentile":{"value":0.9121881,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"16","issue":"6","first_page":"1253","last_page":"1268"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9970999956130981,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/chebyshev-filter","display_name":"Chebyshev filter","score":0.6824209690093994},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6299958229064941},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.548704206943512},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5414054989814758},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5204330086708069},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5106483101844788},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.49339786171913147},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49264460802078247},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4129009246826172},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33468031883239746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1397756040096283}],"concepts":[{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.6824209690093994},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6299958229064941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.548704206943512},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5414054989814758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5204330086708069},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5106483101844788},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.49339786171913147},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49264460802078247},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4129009246826172},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33468031883239746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1397756040096283},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0916073","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0916073","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:casi.ntrs.nasa.gov:19920003815","is_oa":true,"landing_page_url":"http://hdl.handle.net/2060/19920003815","pdf_url":"https://ntrs.nasa.gov/api/citations/19920003815/downloads/19920003815.pdf","source":{"id":"https://openalex.org/S4306402118","display_name":"NASA Technical Reports Server (NASA)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1305493378","host_organization_name":"NASA Headquarters","host_organization_lineage":["https://openalex.org/I1305493378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CASI","raw_type":"NAS 1.26:4411"}],"best_oa_location":{"id":"pmh:oai:casi.ntrs.nasa.gov:19920003815","is_oa":true,"landing_page_url":"http://hdl.handle.net/2060/19920003815","pdf_url":"https://ntrs.nasa.gov/api/citations/19920003815/downloads/19920003815.pdf","source":{"id":"https://openalex.org/S4306402118","display_name":"NASA Technical Reports Server (NASA)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1305493378","host_organization_name":"NASA Headquarters","host_organization_lineage":["https://openalex.org/I1305493378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CASI","raw_type":"NAS 1.26:4411"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","score":0.6100000143051147,"display_name":"No poverty"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2001816900.pdf","grobid_xml":"https://content.openalex.org/works/W2001816900.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W103640377","https://openalex.org/W1912930600","https://openalex.org/W1976990532","https://openalex.org/W1991921299","https://openalex.org/W2097898402","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W4213342932","https://openalex.org/W2056379897","https://openalex.org/W2074316639","https://openalex.org/W2541927208","https://openalex.org/W2478636110","https://openalex.org/W3139814365","https://openalex.org/W3035100220","https://openalex.org/W2073327480"],"abstract_inverted_index":{"We":[0,139],"study":[1],"several":[2,109],"algorithms":[3,111],"for":[4,46,60,108,112,121],"computing":[5,51,62,113],"the":[6,22,25,32,47,52,55,63,66,75,78,83,87,96,102,114,117,154,163,176,186],"Chebyshev":[7,26,118],"spectral":[8],"derivative":[9,53,115],"and":[10,70,134],"compare":[11],"their":[12],"roundoff":[13,84],"error.":[14],"For":[15,168],"a":[16,122,135,147],"large":[17],"number":[18],"of":[19,24,65,77,86,95,101,125,162],"collocation":[20,119],"points,":[21],"elements":[23,64],"differentiation":[27],"matrix,":[28],"if":[29,74],"constructed":[30],"in":[31,174],"usual":[33],"way,":[34],"are":[35,68,80,106],"not":[36,151],"computed":[37,81],"accurately.":[38],"A":[39],"subtle":[40],"cause":[41],"is":[42,90,144,180],"found":[43,181],"to":[44,182],"account":[45],"poor":[48],"accuracy":[49],"when":[50],"by":[54,116],"matrix-vector":[56,88],"multiplication":[57,89],"method.":[58,188],"Methods":[59],"accurately":[61],"matrix":[67,79],"presented":[69],"we":[71],"find":[72,140],"that":[73,94,141],"entries":[76],"accurately,":[82],"error":[85],"as":[91,93,166],"small":[92,160],"transform-recursion":[97,187],"algorithm.":[98],"Furthermore,":[99],"results":[100],"CPU":[103],"time":[104],"usage":[105],"shown":[107],"different":[110],"method":[120],"wide":[123],"variety":[124],"two-dimensional":[126],"grid":[127,155,171],"sizes":[128,172],"on":[129,146,153,159],"both":[130],"an":[131],"IBM":[132],"mainframe":[133],"Cray":[136],"2":[137],"computer.":[138],"which":[142],"algorithm":[143,179],"fastest":[145],"particular":[148],"machine":[149],"depends":[150],"only":[152],"size,":[156],"but":[157],"also":[158],"details":[161],"computer":[164],"hardware":[165],"well.":[167],"most":[169],"practical":[170],"used":[173],"computation,":[175],"even-odd":[177],"decomposition":[178],"be":[183],"faster":[184],"than":[185]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":13}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
