{"id":"https://openalex.org/W1982612743","doi":"https://doi.org/10.1137/030600758","title":"Computation of the Exponential of Large Sparse Skew-Symmetric Matrices","display_name":"Computation of the Exponential of Large Sparse Skew-Symmetric Matrices","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1982612743","doi":"https://doi.org/10.1137/030600758","mag":"1982612743"},"language":"en","primary_location":{"id":"doi:10.1137/030600758","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600758","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/A5005901551","display_name":"Nicoletta Del Buono","orcid":"https://orcid.org/0000-0001-5079-875X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"N. Del Buono","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014483726","display_name":"L. Lopez","orcid":"https://orcid.org/0000-0001-5083-5151"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Lopez","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041079467","display_name":"R. Peluso","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Peluso","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005901551"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3655,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.88311751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"1","first_page":"278","last_page":"293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9835000038146973,"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.7894034385681152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.751815676689148},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5693223476409912},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5661454796791077},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.5562096238136292},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5381669998168945},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.5316112041473389},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.525505542755127},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5058640837669373},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49118754267692566},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.4738771617412567},{"id":"https://openalex.org/keywords/skew-symmetric-matrix","display_name":"Skew-symmetric matrix","score":0.4644925892353058},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.44421109557151794},{"id":"https://openalex.org/keywords/schur-decomposition","display_name":"Schur decomposition","score":0.4147629737854004},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39389604330062866},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3666623830795288},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3237581253051758},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27324074506759644},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.18381258845329285},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17609167098999023},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.13111409544944763},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09178724884986877},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.08175355195999146},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08129703998565674}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.7894034385681152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.751815676689148},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5693223476409912},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5661454796791077},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.5562096238136292},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5381669998168945},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.5316112041473389},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.525505542755127},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5058640837669373},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49118754267692566},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.4738771617412567},{"id":"https://openalex.org/C41106240","wikidata":"https://www.wikidata.org/wiki/Q526790","display_name":"Skew-symmetric matrix","level":5,"score":0.4644925892353058},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.44421109557151794},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.4147629737854004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39389604330062866},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3666623830795288},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3237581253051758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27324074506759644},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.18381258845329285},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17609167098999023},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.13111409544944763},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09178724884986877},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.08175355195999146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08129703998565674},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/030600758","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600758","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"},{"id":"pmh:oai:ricerca.uniba.it:11586/113313","is_oa":false,"landing_page_url":"http://hdl.handle.net/11586/113313","pdf_url":null,"source":{"id":"https://openalex.org/S4377196296","display_name":"CINECA IRIS Institutional Research Information System (University of Bari Aldo Moro)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5561750","host_organization_name":"University of Bari Aldo Moro","host_organization_lineage":["https://openalex.org/I5561750"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W164096006","https://openalex.org/W1488435683","https://openalex.org/W1527992869","https://openalex.org/W1544770838","https://openalex.org/W1584723409","https://openalex.org/W1970935533","https://openalex.org/W1981041413","https://openalex.org/W1984347942","https://openalex.org/W1990753794","https://openalex.org/W2006409769","https://openalex.org/W2025216121","https://openalex.org/W2030512067","https://openalex.org/W2039937805","https://openalex.org/W2041526644","https://openalex.org/W2044543226","https://openalex.org/W2050639649","https://openalex.org/W2057602562","https://openalex.org/W2059586807","https://openalex.org/W2061356302","https://openalex.org/W2077166865","https://openalex.org/W2093091422","https://openalex.org/W2095222360","https://openalex.org/W2134645580","https://openalex.org/W2568342123","https://openalex.org/W2947056241","https://openalex.org/W4237384699"],"related_works":["https://openalex.org/W1601294834","https://openalex.org/W1995120688","https://openalex.org/W2099169296","https://openalex.org/W1798403110","https://openalex.org/W2385506647","https://openalex.org/W2346829627","https://openalex.org/W2082298889","https://openalex.org/W2026897016","https://openalex.org/W2074051898","https://openalex.org/W1982612743"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"methods":[5],"for":[6],"evaluating":[7],"both":[8],"exp(A)":[9,65],"and":[10,34,63,87,96],"$exp(\\tau":[11],"A)q_1$":[12],"where":[13],"${\\rm":[14],"exp}(\\cdot)$":[15],"is":[16,21,30,36,43,50,66],"the":[17,58,83,89],"exponential":[18],"function,":[19],"A":[20,49,86],"a":[22,31,37],"sparse":[23],"skew-symmetric":[24],"matrix":[25],"of":[26,70,75,82,85,88,92],"large":[27],"dimension,":[28],"q1":[29],"given":[32],"vector,":[33],"$\\tau$":[35],"scaling":[38],"factor.":[39],"The":[40,77],"proposed":[41],"method":[42],"based":[44],"on":[45],"two":[46],"main":[47],"steps:":[48],"factorized":[51],"into":[52],"its":[53],"tridiagonal":[54],"form":[55],"H":[56],"by":[57],"well-known":[59],"Lanczos":[60],"iterative":[61],"process,":[62],"then":[64],"derived":[67],"making":[68],"use":[69],"an":[71],"effective":[72],"Schur":[73],"decomposition":[74],"H.":[76],"procedure":[78],"takes":[79],"full":[80],"advantage":[81],"sparsity":[84],"decay":[90],"behavior":[91],"exp(H).":[93],"Several":[94],"applications":[95],"numerical":[97],"tests":[98],"are":[99],"also":[100],"reported.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}