{"id":"https://openalex.org/W1966773805","doi":"https://doi.org/10.1137/0912059","title":"The Fast Gauss Transform with Variable Scales","display_name":"The Fast Gauss Transform with Variable Scales","publication_year":1991,"publication_date":"1991-09-01","ids":{"openalex":"https://openalex.org/W1966773805","doi":"https://doi.org/10.1137/0912059","mag":"1966773805"},"language":"en","primary_location":{"id":"doi:10.1137/0912059","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0912059","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical 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/A5086443955","display_name":"John Strain","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John Strain","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5086443955"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1845,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.76432607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"5","first_page":"1131","last_page":"1139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9905999898910522,"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9905999898910522,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9894000291824341,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.63974529504776},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6091323494911194},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.564516544342041},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5546659827232361},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5523579120635986},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5281130075454712},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.5250037908554077},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49927806854248047},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.46902337670326233},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.46234384179115295},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4163963496685028},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.291908860206604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22477835416793823},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17786094546318054},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09495609998703003},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.08863675594329834},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08333900570869446}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.63974529504776},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6091323494911194},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.564516544342041},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5546659827232361},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5523579120635986},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5281130075454712},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.5250037908554077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49927806854248047},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.46902337670326233},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.46234384179115295},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4163963496685028},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.291908860206604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22477835416793823},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17786094546318054},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09495609998703003},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.08863675594329834},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08333900570869446},{"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0912059","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0912059","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical 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":11,"referenced_works":["https://openalex.org/W136349837","https://openalex.org/W2002735737","https://openalex.org/W2013357098","https://openalex.org/W2018972063","https://openalex.org/W2049343897","https://openalex.org/W2160431995","https://openalex.org/W2315142130","https://openalex.org/W3200698245","https://openalex.org/W4230941884","https://openalex.org/W4233014035","https://openalex.org/W4253808047"],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2027972911","https://openalex.org/W2146343568","https://openalex.org/W2013643406","https://openalex.org/W3157543420","https://openalex.org/W2169866437","https://openalex.org/W1964286703"],"abstract_inverted_index":{"This":[0,21],"paper":[1],"presents":[2],"a":[3,8,56],"fast":[4],"algorithm":[5,22],"that":[6,15],"evaluates":[7,23],"d-dimensional":[9],"Gaussian":[10],"convolution":[11],"sum":[12,25],"with":[13,61],"scales":[14,71],"vary":[16],"from":[17],"point":[18],"to":[19],"point.":[20],"the":[24,44,48,52],"of":[26,51,58],"N":[27],"Gaussians":[28],"at":[29],"M":[30,64],"arbitrarily":[31],"distributed":[32],"points":[33],"in":[34],"$C(N":[35],"+":[36],"M)$":[37],"work,":[38],"where":[39],"C":[40],"depends":[41],"only":[42],"on":[43],"precision":[45],"required":[46],"and":[47,70],"essential":[49],"minimum":[50],"scales.":[53],"It":[54],"achieves":[55],"speedup":[57],"almost":[59],"2,000":[60],"$N":[62],"=":[63,65,68],"100,000$,":[66],"$d":[67],"2$,":[69],"bounded":[72],"below":[73],"by":[74],"$1/100$.":[75]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
