{"id":"https://openalex.org/W2057111517","doi":"https://doi.org/10.1137/040603954","title":"Modeling Test Responses by Multivariable Polynomials of Higher Degrees","display_name":"Modeling Test Responses by Multivariable Polynomials of Higher Degrees","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2057111517","doi":"https://doi.org/10.1137/040603954","mag":"2057111517"},"language":"en","primary_location":{"id":"doi:10.1137/040603954","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040603954","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103293604","display_name":"Jiguan Gene Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"JiGuan G. Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5103293604"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8238,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.7669402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"3","first_page":"832","last_page":"867"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8104590177536011},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7662886381149292},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6032764911651611},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5243040323257446},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5058600306510925},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5036689639091492},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4236091375350952},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4234941005706787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1938382387161255},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14278754591941833},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1149442195892334}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8104590177536011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7662886381149292},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6032764911651611},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5243040323257446},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5058600306510925},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5036689639091492},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4236091375350952},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4234941005706787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1938382387161255},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14278754591941833},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1149442195892334},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040603954","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040603954","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1021555734","https://openalex.org/W1971507640","https://openalex.org/W1979349759","https://openalex.org/W1982471813","https://openalex.org/W1984726321","https://openalex.org/W1987313619","https://openalex.org/W1995791183","https://openalex.org/W2005423095","https://openalex.org/W2027089978","https://openalex.org/W2041559800","https://openalex.org/W2044771513","https://openalex.org/W2056737624","https://openalex.org/W2066169881","https://openalex.org/W2075665712","https://openalex.org/W2078841894","https://openalex.org/W2098502158","https://openalex.org/W2106581481","https://openalex.org/W2116108132","https://openalex.org/W2117026915","https://openalex.org/W2135622428","https://openalex.org/W2583812316","https://openalex.org/W2588215197"],"related_works":["https://openalex.org/W2154249783","https://openalex.org/W2495424399","https://openalex.org/W1515733880","https://openalex.org/W2007040503","https://openalex.org/W4234603592","https://openalex.org/W2890162296","https://openalex.org/W2157340703","https://openalex.org/W2903666957","https://openalex.org/W3047310051","https://openalex.org/W4289117577"],"abstract_inverted_index":{"Engineering":[0],"tests":[1],"generally":[2],"acquire":[3],"a":[4,15,52,193],"large":[5],"set":[6],"of":[7,18,58,111,115,182,188],"response":[8,21,36,128,159],"data":[9,32],"at":[10],"once":[11],"while":[12],"focusing":[13],"on":[14,75,192],"small":[16],"number":[17],"variables.":[19],"Higher-order":[20],"models":[22,38],"are":[23,40],"better":[24],"for":[25,51,63,79,101],"capturing":[26],"and":[27,93,149,166],"displaying":[28],"the":[29,55,59,65,72,81,103,109,125,133,146,162,189],"characteristics":[30],"such":[31],"can":[33,130],"reveal,":[34],"but":[35],"surface":[37],"traditionally":[39,77],"linear":[41],"or":[42,45,99,185],"quadratic":[43],"(first":[44],"second":[46],"order)":[47],"only.":[48],"If":[49],"attempted":[50],"higher":[53],"order,":[54],"matrix":[56,87],"X":[57,76,88,90,116],"test":[60,66],"inputs":[61],"formed":[62],"fitting":[64,156],"responses":[67],"often":[68],"immediately":[69],"stops":[70],"satisfying":[71],"full-rank":[73],"assumption":[74],"made":[78],"computing":[80],"regression":[82,106],"coefficients.":[83],"The":[84,153],"resulting":[85],"product":[86],"T":[89],"is":[91],"singular":[92,140],"hence":[94],"cannot":[95],"be":[96],"inverted,":[97],"directly":[98],"indirectly,":[100],"obtaining":[102],"desired":[104],"least-squares":[105],"coefficients":[107,135,187],"from":[108],"system":[110],"normal":[112],"equations.":[113],"Ill-conditioning":[114],"when":[117],"near":[118],"rank":[119,147,172],"deficiency,":[120],"not":[121],"unusual":[122],"even":[123],"in":[124,174],"traditional":[126],"second-order":[127],"modeling,":[129],"also":[131],"render":[132],"computed":[134],"unreliable.":[136],"This":[137],"paper":[138],"incorporates":[139],"value":[141],"decomposition":[142],"(SVD)":[143],"to":[144,161],"handle":[145],"deficiency":[148,173],"ill-conditioning":[150],"problems":[151],"directly.":[152],"proposed":[154,177],"SVD-based":[155],"algorithm":[157],"enables":[158],"modeling":[160],"desirable":[163],"high-order":[164],"reliably":[165],"efficiently":[167],"with":[168],"no":[169],"difficulty":[170],"despite":[171],"X.":[175],"Two":[176],"trimming":[178],"algorithms":[179],"enable":[180],"reduction":[181],"redundant":[183],"terms":[184],"insignificant":[186],"fitted":[190],"polynomials":[191],"sound":[194],"mathematical":[195],"base.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
