{"id":"https://openalex.org/W2086117135","doi":"https://doi.org/10.1137/s0036142902414542","title":"On the Norms of Inverses of Pseudospectral Differentiation Matrices","display_name":"On the Norms of Inverses of Pseudospectral Differentiation Matrices","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2086117135","doi":"https://doi.org/10.1137/s0036142902414542","mag":"2086117135"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902414542","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902414542","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5060626782","display_name":"D. M. Sloan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David M. Sloan","raw_affiliation_strings":["Mathematics And Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5060626782"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.16267367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"42","issue":"1","first_page":"30","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"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":0.9984999895095825,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9918000102043152,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.991599977016449,"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/mathematics","display_name":"Mathematics","score":0.8803504109382629},{"id":"https://openalex.org/keywords/chebyshev-pseudospectral-method","display_name":"Chebyshev pseudospectral method","score":0.7257230281829834},{"id":"https://openalex.org/keywords/pseudospectral-optimal-control","display_name":"Pseudospectral optimal control","score":0.6831503510475159},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6770710945129395},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.6378672122955322},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.5834833383560181},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5276060104370117},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.48490768671035767},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4566851854324341},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.4550217092037201},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4382704794406891},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4359608590602875},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.41107693314552307},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.3178316056728363},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.11003562808036804},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09118238091468811},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.08827543258666992},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.0666036307811737}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8803504109382629},{"id":"https://openalex.org/C122107654","wikidata":"https://www.wikidata.org/wiki/Q5089017","display_name":"Chebyshev pseudospectral method","level":5,"score":0.7257230281829834},{"id":"https://openalex.org/C154304650","wikidata":"https://www.wikidata.org/wiki/Q7255577","display_name":"Pseudospectral optimal control","level":5,"score":0.6831503510475159},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6770710945129395},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.6378672122955322},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5834833383560181},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5276060104370117},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.48490768671035767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4566851854324341},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.4550217092037201},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4382704794406891},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4359608590602875},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.41107693314552307},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.3178316056728363},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.11003562808036804},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09118238091468811},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.08827543258666992},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0666036307811737},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142902414542","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902414542","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:2192","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/2192/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W256743373","https://openalex.org/W1490180844","https://openalex.org/W1549220217","https://openalex.org/W1558122728","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1982881251","https://openalex.org/W1983412111","https://openalex.org/W2028522134","https://openalex.org/W2051478763","https://openalex.org/W2059998776","https://openalex.org/W2069381275","https://openalex.org/W2073732659","https://openalex.org/W2082987063","https://openalex.org/W2090043357","https://openalex.org/W2131778920","https://openalex.org/W2314359380","https://openalex.org/W2316418224","https://openalex.org/W3021821037","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2550657075","https://openalex.org/W2281601070","https://openalex.org/W2761671048","https://openalex.org/W2143234151","https://openalex.org/W2095947114","https://openalex.org/W2130417219","https://openalex.org/W2080233518","https://openalex.org/W2355904882","https://openalex.org/W1991100480","https://openalex.org/W2294332207"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"give":[4,64],"integral":[5,65],"expressions":[6,66],"for":[7,23,67],"the":[8,11,24,41,51,57],"elements":[9],"of":[10,13,27,53,69],"inverses":[12,68],"second-order":[14],"pseudospectral":[15,72],"differentiation":[16,73],"matrices.":[17,74],"Simple":[18],"upper":[19,45],"bounds":[20,46],"are":[21,35,48,59],"given":[22],"maximum":[25],"norms":[26],"these":[28],"inverse":[29],"matrices":[30],"when":[31,56],"Chebyshev":[32,71],"collocation":[33,54],"points":[34,55,58],"used.":[36],"Comment":[37],"is":[38],"made":[39],"on":[40],"failure":[42],"to":[43],"obtain":[44],"that":[47],"uniform":[49],"in":[50],"number":[52],"evenly":[60],"spaced.":[61],"We":[62],"also":[63],"first-order":[70]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
