{"id":"https://openalex.org/W2024593588","doi":"https://doi.org/10.1090/s0025-5718-01-01384-9","title":"New convergence results on the generalized Richardson extrapolation process GREP\u207d\u00b9\u207e for logarithmic sequences","display_name":"New convergence results on the generalized Richardson extrapolation process GREP\u207d\u00b9\u207e for logarithmic sequences","publication_year":2001,"publication_date":"2001-11-28","ids":{"openalex":"https://openalex.org/W2024593588","doi":"https://doi.org/10.1090/s0025-5718-01-01384-9","mag":"2024593588"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01384-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01384-9","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01384-9/S0025-5718-01-01384-9.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/2002-71-240/S0025-5718-01-01384-9/S0025-5718-01-01384-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067073885","display_name":"Avram Sidi","orcid":"https://orcid.org/0000-0001-6019-2591"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Avram Sidi","raw_affiliation_strings":["Computer Science Department, Technion\u00e2\u0080\u0094Israel Institute of Technology, Haifa 32000, Israel","Computer Science Department, Technion -- Israel Institute of Technology, Haifa 32000, Israel#TAB#"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Technion\u00e2\u0080\u0094Israel Institute of Technology, Haifa 32000, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Computer Science Department, Technion -- Israel Institute of Technology, Haifa 32000, Israel#TAB#","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067073885"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.17250355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"71","issue":"240","first_page":"1569","last_page":"1596"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9973999857902527,"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/combinatorics","display_name":"Combinatorics","score":0.5979573130607605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.509360671043396},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.4985010623931885},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45699992775917053},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.45591461658477783},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3534417152404785},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1635264754295349}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5979573130607605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.509360671043396},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.4985010623931885},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45699992775917053},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.45591461658477783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3534417152404785},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1635264754295349},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-01-01384-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01384-9","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01384-9/S0025-5718-01-01384-9.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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01384-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01384-9","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01384-9/S0025-5718-01-01384-9.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/W2024593588.pdf","grobid_xml":"https://content.openalex.org/works/W2024593588.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W181947251","https://openalex.org/W635817034","https://openalex.org/W1970362786","https://openalex.org/W1974578985","https://openalex.org/W1987082236","https://openalex.org/W2005816214","https://openalex.org/W2005996704","https://openalex.org/W2006720062","https://openalex.org/W2010069926","https://openalex.org/W2011400626","https://openalex.org/W2016580706","https://openalex.org/W2020688938","https://openalex.org/W2038252947","https://openalex.org/W2054246748","https://openalex.org/W2062385224","https://openalex.org/W2079587092","https://openalex.org/W2091663762","https://openalex.org/W2093432799","https://openalex.org/W2122910979","https://openalex.org/W2129973008","https://openalex.org/W2505936072","https://openalex.org/W4233608938","https://openalex.org/W4236296644","https://openalex.org/W4237227248","https://openalex.org/W4238626369","https://openalex.org/W4243470682","https://openalex.org/W6602773775","https://openalex.org/W6636625525","https://openalex.org/W6827478259"],"related_works":["https://openalex.org/W1968270095","https://openalex.org/W2220129715","https://openalex.org/W4296478327","https://openalex.org/W2042397106","https://openalex.org/W4361730764","https://openalex.org/W1965029248","https://openalex.org/W2333625343","https://openalex.org/W1960072520","https://openalex.org/W2023776155","https://openalex.org/W2387596242"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,91,117,140,168,195,215,230,259,291,310],"content-type=\"math/mathml\">":[2,92,118,141,169,196,216,231,260,292,311],"<mml:math":[3,93,119,142,170,197,217,232,261,293,312],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,94,120,143,171,198,218,233,262,294,313],"alttext=\"a":[5,121,314],"left-parenthesis":[6,14,122,145,264,315],"t":[7,15,30,123,146,174,316],"right-parenthesis":[8,16],"tilde":[9],"upper":[10],"A":[11],"plus":[12],"phi":[13],"sigma-summation":[17],"Underscript":[18],"i":[19,28],"equals":[20],"0":[21,97],"Overscript":[22],"normal":[23],"infinity":[24],"Endscripts":[25],"beta":[26],"Subscript":[27,235],"Baseline":[29],"Superscript":[31],"i\">":[32,236],"<mml:semantics>":[33,99,125,148,177,202,221,237,267,297,318],"<mml:mrow>":[34,100,126,149,178,203,319],"<mml:mi>a</mml:mi>":[35,127,320],"<mml:mo":[36,39,49,52,102,128,131,153,156,272,275,321,324],"stretchy=\"false\">(</mml:mo>":[37,50,129,154,273,322],"<mml:mi>t</mml:mi>":[38,51,76,101,130,155,181,323],"stretchy=\"false\">)</mml:mo>":[40,53,132,157,276,325],"<mml:mo>":[41,55,182],"\u223c":[42],"</mml:mo>":[43,57,105,184],"<mml:mi>A</mml:mi>":[44,222,298],"<mml:mo>+</mml:mo>":[45,107],"<mml:mi>":[46,70,150,239],"\u03c6":[47,151],"</mml:mi>":[48,67,72,152,241],"<mml:munderover>":[54],"\u2211":[56],"<mml:mrow":[58,270],"class=\"MJX-TeXAtom-ORD\">":[59,271],"<mml:mi>i</mml:mi>":[60,73,77,242],"<mml:mo>=</mml:mo>":[61],"<mml:mn>0</mml:mn>":[62,106,179,206],"</mml:mrow>":[63,79,108,133,158,186,207,277,326],"<mml:mi":[64],"mathvariant=\"normal\">":[65],"\u221e":[66],"</mml:munderover>":[68],"<mml:msub>":[69,238],"\u03b2":[71,240],"</mml:msub>":[74,243],"<mml:msup>":[75,268],"</mml:msup>":[78,278],"<mml:annotation":[80,109,134,159,187,208,223,244,279,299,327],"encoding=\"application/x-tex\">a(t)\\sim":[81],"A+\\varphi":[82],"(t)\\sum":[83],"^\\infty":[84],"_{i=0}\\beta":[85],"_it^i</mml:annotation>":[86],"</mml:semantics>":[87,112,136,162,190,210,225,247,281,301,329],"</mml:math>":[88,113,137,163,191,211,226,248,282,302],"</inline-formula>":[89,114,138,164,192,212,227,249,283,303],"as":[90],"alttext=\"t":[95],"right-arrow":[96],"plus\">":[98],"stretchy=\"false\">":[103],"\u2192":[104],"encoding=\"application/x-tex\">t\\to":[110],"0+</mml:annotation>":[111],",":[115,213,304],"where":[116],"right-parenthesis\">":[124,147,266,317],"encoding=\"application/x-tex\">a(t)</mml:annotation>":[135,328],"and":[139,228],"alttext=\"phi":[144],"encoding=\"application/x-tex\">\\varphi":[160],"(t)</mml:annotation>":[161],"are":[165,250],"known":[166],"for":[167,193],"alttext=\"0":[172],"greater-than":[173,200],"less-than-or-equal-to":[175],"c\">":[176],"<mml:mo>&gt;</mml:mo>":[180,205],"\u2264":[183],"<mml:mi>c</mml:mi>":[185,204],"encoding=\"application/x-tex\">0&gt;t\\leq":[188],"c</mml:annotation>":[189],"some":[194],"alttext=\"c":[199],"0\">":[201],"encoding=\"application/x-tex\">c&gt;0</mml:annotation>":[209],"but":[214],"alttext=\"upper":[219,295],"A\">":[220,296],"encoding=\"application/x-tex\">A</mml:annotation>":[224,300],"the":[229,305],"alttext=\"beta":[234],"encoding=\"application/x-tex\">\\beta":[245],"_i</mml:annotation>":[246],"not":[251],"known.":[252],"The":[253],"generalized":[254],"Richardson":[255],"extrapolation":[256],"process":[257],"GREP":[258],"alttext=\"Superscript":[263],"1":[265],"<mml:mi/>":[269],"<mml:mn>1</mml:mn>":[274],"encoding=\"application/x-tex\">^{(1)}</mml:annotation>":[280],"is":[284],"used":[285],"in":[286],"obtaining":[287],"good":[288],"approximations":[289],"to":[290],"limit":[306],"or":[307],"antilimit":[308],"of":[309]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
