{"id":"https://openalex.org/W2079559649","doi":"https://doi.org/10.1137/s1064827592240555","title":"Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix","display_name":"Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix","publication_year":1997,"publication_date":"1997-07-01","ids":{"openalex":"https://openalex.org/W2079559649","doi":"https://doi.org/10.1137/s1064827592240555","mag":"2079559649"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827592240555","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827592240555","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/A5110155185","display_name":"C. R. Dietrich","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"C. R. Dietrich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023554201","display_name":"Garry N. Newsam","orcid":"https://orcid.org/0000-0002-4492-3048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. N. Newsam","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110155185"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7318,"has_fulltext":false,"cited_by_count":529,"citation_normalized_percentile":{"value":0.92552435,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"18","issue":"4","first_page":"1088","last_page":"1107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9772999882698059,"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/T10716","display_name":"Soil and Unsaturated Flow","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.8829400539398193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8228694796562195},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.7494938969612122},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7100643515586853},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7096003890037537},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5959842801094055},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5808408856391907},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.563077449798584},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5308554768562317},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5159200429916382},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.46965256333351135},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4574129283428192},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.45117276906967163},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3725792169570923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3648551404476166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28575992584228516},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2133912742137909},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12701383233070374},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09904283285140991},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07329270243644714}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8829400539398193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8228694796562195},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.7494938969612122},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7100643515586853},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7096003890037537},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5959842801094055},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5808408856391907},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.563077449798584},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5308554768562317},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5159200429916382},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.46965256333351135},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4574129283428192},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.45117276906967163},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3725792169570923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3648551404476166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28575992584228516},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2133912742137909},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12701383233070374},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09904283285140991},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07329270243644714},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/s1064827592240555","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827592240555","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W119461825","https://openalex.org/W178392745","https://openalex.org/W1558542711","https://openalex.org/W1967639991","https://openalex.org/W1978134494","https://openalex.org/W1978473169","https://openalex.org/W1987656037","https://openalex.org/W1993931698","https://openalex.org/W2004973936","https://openalex.org/W2006915601","https://openalex.org/W2011157831","https://openalex.org/W2017769677","https://openalex.org/W2037942041","https://openalex.org/W2043099482","https://openalex.org/W2048902846","https://openalex.org/W2050427484","https://openalex.org/W2056842996","https://openalex.org/W2067737711","https://openalex.org/W2069650072","https://openalex.org/W2079321251","https://openalex.org/W2112498056","https://openalex.org/W2113325425","https://openalex.org/W2115125420","https://openalex.org/W2120062331","https://openalex.org/W2129752419","https://openalex.org/W2145689771","https://openalex.org/W2153700325","https://openalex.org/W2169214897","https://openalex.org/W2171313876","https://openalex.org/W2226040954","https://openalex.org/W3119264854","https://openalex.org/W3148924112","https://openalex.org/W3216259776","https://openalex.org/W4241089600"],"related_works":["https://openalex.org/W3177828492","https://openalex.org/W2034415022","https://openalex.org/W2149698301","https://openalex.org/W4388372565","https://openalex.org/W63525287","https://openalex.org/W2286689764","https://openalex.org/W2026406497","https://openalex.org/W4388372654","https://openalex.org/W2105266774","https://openalex.org/W1444802581"],"abstract_inverted_index":{"Geostatistical":[0],"simulations":[1,140],"often":[2],"require":[3],"the":[4,34,48,66,71,98,127],"generation":[5],"of":[6,9,33,50,54,65,97,110,141],"numerous":[7],"realizations":[8,32,96],"a":[10,15,42,88],"stationary":[11,142],"Gaussian":[12],"process":[13,36],"over":[14,37],"regularly":[16],"meshed":[17],"sample":[18],"grid":[19],"$\\Omega$.":[20],"This":[21],"paper":[22,72],"shows":[23],"that":[24,75,120],"for":[25,121],"many":[26,122],"important":[27],"correlation":[28,81,125],"functions":[29],"in":[30,87,130,144],"geostatistics,":[31],"associated":[35],"$m+1$":[38],"equispaced":[39],"points":[40],"on":[41],"line":[43],"can":[44,84,105],"be":[45,85,106],"produced":[46],"at":[47],"cost":[49],"an":[51,62,77],"initial":[52],"FFT":[53,64],"length":[55,111],"$2m$":[56],"with":[57],"each":[58],"new":[59],"realization":[60],"requiring":[61],"additional":[63],"same":[67],"length.":[68],"In":[69],"particular,":[70],"first":[73],"notes":[74],"if":[76],"$(m+1)\\times(m+1)":[78],"$":[79],"Toeplitz":[80],"matrix":[82,93],"R":[83],"embedded":[86],"nonnegative":[89,136],"definite":[90],"$2M\\times2M$":[91],"circulant":[92],"S,":[94],"exact":[95],"normal":[99],"multivariate":[100],"$y":[101],"\\sim":[102],"{\\cal":[103],"N}(0,R)$":[104],"generated":[107],"via":[108],"FFTs":[109],"$2M$.":[112],"Theoretical":[113],"results":[114],"are":[115,147],"then":[116],"presented":[117],"to":[118,139],"demonstrate":[119],"commonly":[123],"used":[124],"structures":[126],"minimal":[128],"embedding":[129],"which":[131],"$M":[132],"=":[133],"m$":[134],"is":[135],"definite.":[137],"Extensions":[138],"fields":[143],"higher":[145],"dimensions":[146],"also":[148],"provided":[149],"and":[150],"illustrated.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":23},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":20},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":49},{"year":2019,"cited_by_count":35},{"year":2018,"cited_by_count":38},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":36},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":32},{"year":2012,"cited_by_count":18}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}