{"id":"https://openalex.org/W2021656599","doi":"https://doi.org/10.1137/s1064827594274607","title":"Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique","display_name":"Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique","publication_year":1997,"publication_date":"1997-07-01","ids":{"openalex":"https://openalex.org/W2021656599","doi":"https://doi.org/10.1137/s1064827594274607","mag":"2021656599"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827594274607","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827594274607","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://conservancy.umn.edu/bitstreams/9466ea81-424d-4b70-ac68-a6a28238f3e7/download","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":4.1336,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.93996009,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"4","first_page":"1040","last_page":"1055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9993000030517578,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9993000030517578,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9980999827384949,"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/chebyshev-filter","display_name":"Chebyshev filter","score":0.758503794670105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7277308106422424},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.7018559575080872},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.6624438166618347},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.6567522287368774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5041729211807251},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4873424470424652},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4726478159427643},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.440701961517334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42546117305755615},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.41173601150512695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3239782452583313},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15876293182373047}],"concepts":[{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.758503794670105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7277308106422424},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.7018559575080872},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.6624438166618347},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.6567522287368774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5041729211807251},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4873424470424652},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4726478159427643},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.440701961517334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42546117305755615},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.41173601150512695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3239782452583313},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15876293182373047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1064827594274607","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827594274607","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:conservancy.umn.edu:11299/2604","is_oa":true,"landing_page_url":"http://purl.umn.edu/2604","pdf_url":"https://conservancy.umn.edu/bitstreams/9466ea81-424d-4b70-ac68-a6a28238f3e7/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.4573","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.4573","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ima.umn.edu/preprints/July1994/1236.ps","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/2604","is_oa":true,"landing_page_url":"http://purl.umn.edu/2604","pdf_url":"https://conservancy.umn.edu/bitstreams/9466ea81-424d-4b70-ac68-a6a28238f3e7/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2021656599.pdf","grobid_xml":"https://content.openalex.org/works/W2021656599.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1971633068","https://openalex.org/W2001816900","https://openalex.org/W2053987390","https://openalex.org/W2078768478","https://openalex.org/W2097898402"],"related_works":["https://openalex.org/W2112919228","https://openalex.org/W2136992695","https://openalex.org/W2021099221","https://openalex.org/W2054912819","https://openalex.org/W2039550572","https://openalex.org/W2179563627","https://openalex.org/W2025308149","https://openalex.org/W1974138590","https://openalex.org/W2345201752","https://openalex.org/W2034868998"],"abstract_inverted_index":{"A":[0],"new":[1],"method":[2],"is":[3,52,58],"investigated":[4],"to":[5,47,112,121],"reduce":[6],"the":[7,28,32,35,39,53,59,92,102,116,140],"roundoff":[8,36,68,124],"error":[9,37,69],"in":[10,79],"computing":[11,80],"derivatives":[12,84],"using":[13,18],"Chebyshev":[14,72,94,104,142],"collocation":[15,62],"methods.":[16],"By":[17],"a":[19,114],"grid":[20],"mapping":[21],"derived":[22],"by":[23,123],"Kosloff":[24],"and":[25,27,56,126],"Tal-Ezer,":[26],"proper":[29],"choice":[30],"of":[31,38,61,67,91,139],"parameter":[33],"$\\alpha$,":[34],"kth":[40],"derivative":[41],"can":[42,130,144],"be":[43,131,145],"reduced":[44],"from":[45],"$O(N^{2k})$":[46],"$O((N":[48],"\\lge)^k)$,":[49],"where":[50],"$\\epsilon$":[51],"machine":[54],"precision":[55],"N":[57],"number":[60],"points.":[63],"This":[64],"drastic":[65],"reduction":[66],"makes":[70],"mapped":[71,93,103,141],"methods":[73,105,143],"competitive":[74],"with":[75,85],"any":[76],"other":[77,89],"algorithm":[78],"second":[81],"or":[82],"higher":[83],"large":[86],"N.":[87],"Several":[88],"aspects":[90],"differentiation":[95],"matrix":[96],"are":[97,118],"also":[98],"studied,":[99],"revealing":[100],"that":[101],"require":[106],"much":[107],"less":[108,119],"than":[109],"$\\pi$":[110],"points":[111],"resolve":[113],"wave;":[115],"eigenvalues":[117],"sensitive":[120],"perturbation":[122],"error;":[125],"larger":[127],"time":[128],"steps":[129],"used":[132],"for":[133],"solving":[134],"PDEs.":[135],"All":[136],"these":[137],"advantages":[138],"achieved":[146],"while":[147],"maintaining":[148],"spectral":[149],"accuracy.":[150]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
