{"id":"https://openalex.org/W2079178182","doi":"https://doi.org/10.1090/s0025-5718-06-01855-2","title":"Orthogonal polynomials for refinable linear functionals","display_name":"Orthogonal polynomials for refinable linear functionals","publication_year":2006,"publication_date":"2006-05-23","ids":{"openalex":"https://openalex.org/W2079178182","doi":"https://doi.org/10.1090/s0025-5718-06-01855-2","mag":"2079178182"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01855-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01855-2","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01855-2/S0025-5718-06-01855-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01855-2/S0025-5718-06-01855-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109847574","display_name":"Dirk Laurie","orcid":null},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Dirk Laurie","raw_affiliation_strings":["Department of Mathematics, University of Stellenbosch, South Africa","[Department of Mathematics, University of Stellenbosch, South Africa]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Stellenbosch, South Africa","institution_ids":["https://openalex.org/I26092322"]},{"raw_affiliation_string":"[Department of Mathematics, University of Stellenbosch, South Africa]","institution_ids":["https://openalex.org/I26092322"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107838272","display_name":"Johan de Villiers","orcid":null},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Johan de Villiers","raw_affiliation_strings":["Department of Mathematics, University of Stellenbosch, South Africa","[Department of Mathematics, University of Stellenbosch, South Africa]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Stellenbosch, South Africa","institution_ids":["https://openalex.org/I26092322"]},{"raw_affiliation_string":"[Department of Mathematics, University of Stellenbosch, South Africa]","institution_ids":["https://openalex.org/I26092322"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109847574"],"corresponding_institution_ids":["https://openalex.org/I26092322"],"apc_list":null,"apc_paid":null,"fwci":2.0217,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86476569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"75","issue":"256","first_page":"1891","last_page":"1903"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematics","display_name":"Mathematics","score":0.6538143157958984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5219530463218689},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.48249244689941406},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.46960175037384033},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45168834924697876},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4215618371963501},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4213699698448181},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21254727244377136},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.17064592242240906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07420691847801208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6538143157958984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5219530463218689},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48249244689941406},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.46960175037384033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45168834924697876},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4215618371963501},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4213699698448181},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21254727244377136},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.17064592242240906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07420691847801208},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-06-01855-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01855-2","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01855-2/S0025-5718-06-01855-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.8127","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.8127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2006-75-256/S0025-5718-06-01855-2/S0025-5718-06-01855-2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01855-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01855-2","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01855-2/S0025-5718-06-01855-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2079178182.pdf","grobid_xml":"https://content.openalex.org/works/W2079178182.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1490272990","https://openalex.org/W1562711392","https://openalex.org/W1593505867","https://openalex.org/W1922505179","https://openalex.org/W1966268321","https://openalex.org/W1994680478","https://openalex.org/W2000225522","https://openalex.org/W2000430190","https://openalex.org/W2001343343","https://openalex.org/W2014114127","https://openalex.org/W2020328455","https://openalex.org/W2055223705","https://openalex.org/W2076377571","https://openalex.org/W2076399337","https://openalex.org/W2115970157","https://openalex.org/W2155632587","https://openalex.org/W2162870748","https://openalex.org/W2794268068"],"related_works":["https://openalex.org/W1976679120","https://openalex.org/W2377519369","https://openalex.org/W3202311233","https://openalex.org/W4281614748","https://openalex.org/W32024214","https://openalex.org/W2765883196","https://openalex.org/W2034826746","https://openalex.org/W2396919090","https://openalex.org/W2081131590","https://openalex.org/W2042326540"],"abstract_inverted_index":{"A":[0],"refinable":[1,39,98,115],"linear":[2],"functional":[3,52,99],"is":[4,53,162],"one":[5],"that":[6,67,160],"can":[7,151],"be":[8],"expressed":[9],"as":[10],"a":[11,17,38,45,51,114],"convex":[12],"combination":[13],"and":[14,26,83],"defined":[15],"by":[16,37,77],"finite":[18],"number":[19],"of":[20,23,29,87,95],"mask":[21,81,102,110],"coefficients":[22,59,76,103],"certain":[24],"stretched":[25],"shifted":[27],"replicas":[28],"itself.":[30],"The":[31,41,117],"notion":[32],"generalizes":[33],"an":[34],"integral":[35],"weighted":[36],"function.":[40,116],"key":[42],"to":[43,54,66,72],"calculating":[44],"Gaussian":[46],"quadrature":[47],"formula":[48],"for":[49,60],"such":[50],"find":[55],"the":[56,61,74,80,85,93,96,101,108],"three-term":[57],"recursion":[58,75],"polynomials":[62],"orthogonal":[63],"with":[64],"respect":[65],"functional.":[68],"We":[69],"show":[70],"how":[71],"obtain":[73],"using":[78],"only":[79],"coefficients,":[82],"without":[84],"aid":[86],"modified":[88],"moments.":[89],"Our":[90],"result":[91],"implies":[92],"existence":[94],"corresponding":[97],"whenever":[100],"are":[104],"nonnegative,":[105],"even":[106],"when":[107],"same":[109],"does":[111],"not":[112],"define":[113],"algorithm":[118],"requires":[119],"<inline-formula":[120],"content-type=\"math/mathml\">":[121],"<mml:math":[122],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[123],"alttext=\"upper":[124],"O":[125],"left-parenthesis":[126],"n":[127],"squared":[128],"right-parenthesis\">":[129],"<mml:semantics>":[130],"<mml:mrow>":[131],"<mml:mi>O</mml:mi>":[132],"<mml:mo":[133,139],"stretchy=\"false\">(</mml:mo>":[134],"<mml:msup>":[135],"<mml:mi>n</mml:mi>":[136],"<mml:mn>2</mml:mn>":[137],"</mml:msup>":[138],"stretchy=\"false\">)</mml:mo>":[140],"</mml:mrow>":[141],"<mml:annotation":[142],"encoding=\"application/x-tex\">O(n^2)</mml:annotation>":[143],"</mml:semantics>":[144],"</mml:math>":[145],"</inline-formula>":[146],"rational":[147],"operations":[148],"and,":[149],"thus,":[150],"in":[152,165],"principle":[153],"deliver":[154],"exact":[155],"results.":[156],"Numerical":[157],"evidence":[158],"suggests":[159],"it":[161],"also":[163],"effective":[164],"floating-point":[166],"arithmetic.":[167]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
