{"id":"https://openalex.org/W1978798278","doi":"https://doi.org/10.1090/s0025-5718-98-00975-2","title":"Fast algorithms for discrete polynomial transforms","display_name":"Fast algorithms for discrete polynomial transforms","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1978798278","doi":"https://doi.org/10.1090/s0025-5718-98-00975-2","mag":"1978798278"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-98-00975-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00975-2","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00975-2/S0025-5718-98-00975-2.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00975-2/S0025-5718-98-00975-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020926962","display_name":"Daniel Potts","orcid":"https://orcid.org/0000-0003-3651-4364"},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Daniel Potts","raw_affiliation_strings":["Fachbereich Mathematik, Universit\u00c3\u00a4t Rostock, D\u00e2\u0080\u009318051 Rostock","Fachbereich Mathematik, Universit\u00e4t Rostock, D\u201318051 Rostock"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00c3\u00a4t Rostock, D\u00e2\u0080\u009318051 Rostock","institution_ids":["https://openalex.org/I4665924"]},{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00e4t Rostock, D\u201318051 Rostock","institution_ids":["https://openalex.org/I4665924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102760434","display_name":"Gabriele Steidl","orcid":"https://orcid.org/0000-0001-7486-6315"},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gabriele Steidl","raw_affiliation_strings":["Fakult\u00c3\u00a4t f\u00c3\u00bcr Mathematik und Informatik, Universit\u00c3\u00a4t Mannheim, D\u00e2\u0080\u009368131 Mannheim","Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Mannheim, D\u201368131 Mannheim"],"affiliations":[{"raw_affiliation_string":"Fakult\u00c3\u00a4t f\u00c3\u00bcr Mathematik und Informatik, Universit\u00c3\u00a4t Mannheim, D\u00e2\u0080\u009368131 Mannheim","institution_ids":["https://openalex.org/I177802217"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Mannheim, D\u201368131 Mannheim","institution_ids":["https://openalex.org/I177802217"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086505493","display_name":"Manfred Tasche","orcid":null},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Manfred Tasche","raw_affiliation_strings":["Fachbereich Mathematik, Universit\u00c3\u00a4t Rostock, D\u00e2\u0080\u009318051 Rostock","Fachbereich Mathematik, Universit\u00e4t Rostock, D\u201318051 Rostock"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00c3\u00a4t Rostock, D\u00e2\u0080\u009318051 Rostock","institution_ids":["https://openalex.org/I4665924"]},{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00e4t Rostock, D\u201318051 Rostock","institution_ids":["https://openalex.org/I4665924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020926962"],"corresponding_institution_ids":["https://openalex.org/I4665924"],"apc_list":null,"apc_paid":null,"fwci":2.0342,"has_fulltext":true,"cited_by_count":101,"citation_normalized_percentile":{"value":0.85315355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"67","issue":"224","first_page":"1577","last_page":"1590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9951000213623047,"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/algorithm","display_name":"Algorithm","score":0.656619131565094},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36074763536453247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2603679299354553}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.656619131565094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36074763536453247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2603679299354553}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-98-00975-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00975-2","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00975-2/S0025-5718-98-00975-2.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:4113","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Potts=3ADaniel=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.3123","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.3123","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/1998-67-224/S0025-5718-98-00975-2/S0025-5718-98-00975-2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3783","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3783","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/journals/mcom/1998-67-224/S0025-5718-98-00975-2/S0025-5718-98-00975-2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.52.5703","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.5703","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.mu-luebeck.de/workers/potts/paper/polynomtrans.ps.Z","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00975-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00975-2","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-00975-2/S0025-5718-98-00975-2.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":null,"license_id":null,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1978798278.pdf","grobid_xml":"https://content.openalex.org/works/W1978798278.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W454695","https://openalex.org/W1966268321","https://openalex.org/W1990415201","https://openalex.org/W1996794064","https://openalex.org/W2000827034","https://openalex.org/W2005998530","https://openalex.org/W2013943932","https://openalex.org/W2031614119","https://openalex.org/W2052169332","https://openalex.org/W2054796168","https://openalex.org/W2064425328","https://openalex.org/W2064988984","https://openalex.org/W2076747309","https://openalex.org/W2077458232","https://openalex.org/W2088086218","https://openalex.org/W2091715500","https://openalex.org/W2149599446","https://openalex.org/W2160615084","https://openalex.org/W3216957337","https://openalex.org/W4237941720","https://openalex.org/W4256167030"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2947381795"],"abstract_inverted_index":{"Consider":[0],"the":[1,93,138,282,285,461,518,522],"Vandermonde-like":[2],"matrix":[3],"<inline-formula":[4,95,119,141,160,184,288,315,362,389,490,530],"content-type=\"math/mathml\">":[5,96,120,142,161,185,289,316,363,390,491,531],"<mml:math":[6,97,121,143,162,186,290,317,364,391,492,532],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,98,122,144,163,187,291,318,365,392,493,533],"alttext=\"bold":[8,164,188,292,366,393,494],"upper":[9,14,25,37,165,189,192,206,217,293,322,326,367,394,397,495],"P":[10,15,100,124,294,368,496],"colon":[11,197],"equals":[12,34,198,214],"left-parenthesis":[13,19,199,321],"Subscript":[16,30,101,125,147,191,210,396],"k":[17,33,203,213],"Baseline":[18,196,401],"cosine":[20,200,453],"StartFraction":[21,201],"j":[22,31,202,211],"pi":[23,204],"Over":[24,205],"N":[26,193,207,323,327,398,535],"EndFraction":[27,208],"right-parenthesis":[28,29,209],"comma":[32,212],"0":[35,215],"Superscript":[36,216],"N\">":[38,218],"<mml:semantics>":[39,103,127,149,167,219,297,329,371,405,499,538],"<mml:mrow>":[40,61,220,243,330,406,539],"<mml:mrow":[41,43,72,168,170,222,224,230,253,298,300,372,374,408,410,416,423,425,427,500,502],"class=\"MJX-TeXAtom-ORD\">":[42,44,73,169,171,223,225,231,254,299,301,373,375,409,411,417,424,426,428,501,503],"<mml:mi":[45,172,226,302,304,376,378,412,430,504,506],"mathvariant=\"bold\">P</mml:mi>":[46,173,303,377,505],"</mml:mrow>":[47,48,64,79,82,174,175,228,229,235,247,260,263,306,307,343,380,381,414,415,421,436,437,438,439,508,509,543],"<mml:mo>:=</mml:mo>":[49,237],"<mml:mo":[50,56,67,70,238,251,332,341,432],"stretchy=\"false\">(</mml:mo>":[51,57,239,333],"<mml:msub>":[52,104,128,150,221,407],"<mml:mi>P</mml:mi>":[53,105,129],"<mml:mi>k</mml:mi>":[54,76,106,130,152,245,257],"</mml:msub>":[55,107,131,153,236,422],"<mml:mi>cos</mml:mi>":[58,240],"<mml:mo>\u2061</mml:mo>":[59,241,339],"<mml:mfrac>":[60,242],"<mml:mi>j</mml:mi>":[62,74,244,255],"<mml:mi>\u03c0</mml:mi>":[63,246],"<mml:mi>N</mml:mi>":[65,80,232,248,261,334,340,418,540],"</mml:mfrac>":[66,249],"stretchy=\"false\">)</mml:mo>":[68,71,252,342],"<mml:msubsup>":[69,250],"<mml:mo>,</mml:mo>":[75,256],"<mml:mo>=</mml:mo>":[77,258],"<mml:mn>0</mml:mn>":[78,259],"</mml:msubsup>":[81,262],"<mml:annotation":[83,108,132,154,176,264,308,344,382,440,510,544],"encoding=\"application/x-tex\">{\\mathbf":[84,177,265,309,383,441,511],"{P}}:=(P_k(\\cos":[85],"\\frac":[86,268],"{j\\pi":[87],"}{N}))_{j,k=0}^N</mml:annotation>":[88],"</mml:semantics>":[89,110,134,156,179,271,311,348,385,446,513,547],"</mml:math>":[90,111,135,157,180,272,312,349,386,447,514,548],"</inline-formula>,":[91,158],"where":[92],"polynomials":[94,140,475],"alttext=\"upper":[99,123,145,319,534],"k\">":[102,126,148],"encoding=\"application/x-tex\">P_k</mml:annotation>":[109,133],"</inline-formula>":[112,136,181,313,350,387,448,515],"satisfy":[113],"a":[114,277,357,403,450,466],"three-term":[115],"recurrence":[116],"relation.":[117],"If":[118],"are":[137],"Chebyshev":[139],"T":[146],"<mml:mi>T</mml:mi>":[151],"encoding=\"application/x-tex\">T_k</mml:annotation>":[155],"then":[159],"P\">":[166],"{P}}</mml:annotation>":[178],"coincides":[182],"with":[183,388,516],"C":[190,395],"plus":[194,399],"1":[195,400],"mathvariant=\"bold\">C</mml:mi>":[227,413],"<mml:mo>+</mml:mo>":[233,419],"<mml:mn>1</mml:mn>":[234,420],"{C}}_{N+1}:=":[266],"(\\cos":[267],"{jk\\pi":[269],"}{N})_{j,k=0}^N</mml:annotation>":[270],"</inline-formula>.":[273,549],"This":[274],"paper":[275],"presents":[276],"new":[278],"fast":[279,358,452,478,486],"algorithm":[280,354,462],"for":[281,529],"computation":[283],"of":[284,460,473],"matrix-vector":[286],"product":[287],"bold":[295,369,402,497],"a\">":[296,370,498],"mathvariant=\"bold\">a</mml:mi>":[305,379,431,507],"{Pa}}</mml:annotation>":[310,384,512],"in":[314],"O":[320],"log":[324],"squared":[325],"right-parenthesis\">":[328],"<mml:mi>O</mml:mi>":[331],"<mml:msup>":[335],"<mml:mi>log</mml:mi>":[336],"<mml:mn>2</mml:mn>":[337],"</mml:msup>":[338],"encoding=\"application/x-tex\">O(N":[345],"\\log":[346],"^2N)</mml:annotation>":[347],"arithmetical":[351],"operations.":[352],"The":[353,455],"divides":[355],"into":[356],"transform":[359,488],"which":[360],"replaces":[361],"overTilde\">":[404],"<mml:mover>":[429],"mathvariant=\"bold\"":[433],"stretchy=\"false\">~</mml:mo>":[434],"</mml:mover>":[435],"{C}}_{N+1}":[442],"{\\mathbf":[443],"{\\tilde":[444],"a}}</mml:annotation>":[445],"and":[449,457,476],"subsequent":[451],"transform.":[454],"first":[456],"central":[458],"part":[459],"is":[463,526],"realized":[464],"by":[465,477],"straightforward":[467],"cascade":[468],"summation":[469],"based":[470],"on":[471],"properties":[472],"associated":[474],"polynomial":[479,487],"multiplications.":[480],"Numerical":[481],"tests":[482],"demonstrate":[483],"that":[484],"our":[485],"realizes":[489],"almost":[517],"same":[519],"precision":[520],"as":[521],"Clenshaw":[523],"algorithm,":[524],"but":[525],"much":[527],"faster":[528],"greater-than-or-equal-to":[536],"128\">":[537],"<mml:mo>\u2265</mml:mo>":[541],"<mml:mn>128</mml:mn>":[542],"encoding=\"application/x-tex\">N\\ge":[545],"128</mml:annotation>":[546]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}