{"id":"https://openalex.org/W2125166189","doi":"https://doi.org/10.1109/cdc.2005.1583117","title":"Laplace and Cayley transforms – an approximation point of view","display_name":"Laplace and Cayley transforms – an approximation point of view","publication_year":2006,"publication_date":"2006-10-04","ids":{"openalex":"https://openalex.org/W2125166189","doi":"https://doi.org/10.1109/cdc.2005.1583117","mag":"2125166189"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2005.1583117","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583117","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5086414326","display_name":"Ville Havu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Havu","raw_affiliation_strings":["Insitute of Mathematics, TKK, Helsinki University of Technology, Finland","Insitute of Mathematics, TKK, Box 1100 FI-02015, Helsinki University of Technology, Finland. Ville.Havu@tkk.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Insitute of Mathematics, TKK, Helsinki University of Technology, Finland","institution_ids":[]},{"raw_affiliation_string":"Insitute of Mathematics, TKK, Box 1100 FI-02015, Helsinki University of Technology, Finland. Ville.Havu@tkk.fi","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081417088","display_name":"Jarmo Malinen","orcid":"https://orcid.org/0000-0001-9117-8450"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"J. Malinen","raw_affiliation_strings":["Insitute of Mathematics, TKK, Helsinki University of Technology, Finland","Aalto University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Insitute of Mathematics, TKK, Helsinki University of Technology, Finland","institution_ids":[]},{"raw_affiliation_string":"Aalto University","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5016,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67556623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":null,"first_page":"5971","last_page":"5976"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/laplace-transform","display_name":"Laplace transform","score":0.8339126706123352},{"id":"https://openalex.org/keywords/laplace-transform-applied-to-differential-equations","display_name":"Laplace transform applied to differential equations","score":0.7253395915031433},{"id":"https://openalex.org/keywords/two-sided-laplace-transform","display_name":"Two-sided Laplace transform","score":0.6936529278755188},{"id":"https://openalex.org/keywords/inverse-laplace-transform","display_name":"Inverse Laplace transform","score":0.6090058088302612},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6067007780075073},{"id":"https://openalex.org/keywords/cayley-transform","display_name":"Cayley transform","score":0.5779685974121094},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5681844353675842},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.540611743927002},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5039977431297302},{"id":"https://openalex.org/keywords/laplace\u2013stieltjes-transform","display_name":"Laplace\u2013Stieltjes transform","score":0.44184941053390503},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4295057952404022},{"id":"https://openalex.org/keywords/mellin-transform","display_name":"Mellin transform","score":0.42803168296813965},{"id":"https://openalex.org/keywords/greens-function-for-the-three-variable-laplace-equation","display_name":"Green's function for the three-variable Laplace equation","score":0.4195685386657715},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.201065331697464},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.1112355887889862}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.8339126706123352},{"id":"https://openalex.org/C194330524","wikidata":"https://www.wikidata.org/wiki/Q2858841","display_name":"Laplace transform applied to differential equations","level":3,"score":0.7253395915031433},{"id":"https://openalex.org/C10288518","wikidata":"https://www.wikidata.org/wiki/Q1785576","display_name":"Two-sided Laplace transform","level":5,"score":0.6936529278755188},{"id":"https://openalex.org/C60455284","wikidata":"https://www.wikidata.org/wiki/Q2162701","display_name":"Inverse Laplace transform","level":3,"score":0.6090058088302612},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6067007780075073},{"id":"https://openalex.org/C18586221","wikidata":"https://www.wikidata.org/wiki/Q2778065","display_name":"Cayley transform","level":5,"score":0.5779685974121094},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5681844353675842},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.540611743927002},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5039977431297302},{"id":"https://openalex.org/C141255357","wikidata":"https://www.wikidata.org/wiki/Q3997728","display_name":"Laplace\u2013Stieltjes transform","level":5,"score":0.44184941053390503},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4295057952404022},{"id":"https://openalex.org/C199874217","wikidata":"https://www.wikidata.org/wiki/Q606934","display_name":"Mellin transform","level":3,"score":0.42803168296813965},{"id":"https://openalex.org/C208067445","wikidata":"https://www.wikidata.org/wiki/Q5602166","display_name":"Green's function for the three-variable Laplace equation","level":4,"score":0.4195685386657715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.201065331697464},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.1112355887889862},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"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/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2005.1583117","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583117","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.419.5548","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.419.5548","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hut.fi/~jmalinen/MyPSFilesInWeb/HavuMalinenEcc05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.81.5803","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.81.5803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.hut.fi/~jmalinen/MyPSFilesInWeb/0761.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1537639429","https://openalex.org/W1998929123","https://openalex.org/W2029860200","https://openalex.org/W2069850951","https://openalex.org/W2113497339","https://openalex.org/W2607777600","https://openalex.org/W4294678829","https://openalex.org/W6667612214","https://openalex.org/W6736675993"],"related_works":["https://openalex.org/W193874820","https://openalex.org/W3022275705","https://openalex.org/W3166878184","https://openalex.org/W4389482554","https://openalex.org/W3027042443","https://openalex.org/W3021788336","https://openalex.org/W4239388564","https://openalex.org/W4283576291","https://openalex.org/W971990890","https://openalex.org/W4213365297"],"abstract_inverted_index":{"We":[0,43],"interpret":[1],"the":[2,31,39,46,58],"Cayley":[3],"transform":[4],"of":[5,17,48,57],"linear":[6],"(finite-or":[7],"infinite-dimensional)":[8],"state":[9],"space":[10],"systems":[11],"as":[12],"a":[13,22,27],"numerical":[14],"integration":[15,50],"scheme":[16,23,51],"Crank\u2013Nicolson":[18],"type.":[19],"If":[20],"such":[21],"is":[24,36,52],"applied":[25],"to":[26,54],"conservative":[28,37],"system,":[29],"then":[30],"resulting":[32],"discrete":[33,40],"time":[34,41],"system":[35],"in":[38],"sense.":[42],"show":[44],"that":[45],"convergence":[47],"this":[49],"equivalent":[53],"an":[55],"approximation":[56],"Laplace":[59],"transform.":[60]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}