{"id":"https://openalex.org/W1973803392","doi":"https://doi.org/10.1155/2012/634698","title":"Approximation of the<i>p</i>th Roots of a Matrix by Using Trapezoid Rule","display_name":"Approximation of the<i>p</i>th Roots of a Matrix by Using Trapezoid Rule","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1973803392","doi":"https://doi.org/10.1155/2012/634698","mag":"1973803392"},"language":"en","primary_location":{"id":"doi:10.1155/2012/634698","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/634698","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/634698.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/634698.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051019262","display_name":"Amir Sadeghi","orcid":"https://orcid.org/0000-0001-8720-1136"},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Amir Sadeghi","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"],"raw_orcid":"https://orcid.org/0000-0001-8720-1136","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059761045","display_name":"A. I. Md. Ismail","orcid":"https://orcid.org/0000-0002-4876-5462"},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Ahmad Izani Md. Ismail","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-4876-5462","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051019262"],"corresponding_institution_ids":["https://openalex.org/I139322472"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.06753542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9879999756813049,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9858999848365784,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8946106433868408},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6383534669876099},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5760533809661865},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5300689935684204},{"id":"https://openalex.org/keywords/cauchys-integral-formula","display_name":"Cauchy's integral formula","score":0.5056414604187012},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.441513329744339},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4398479163646698},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42758530378341675},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3625979721546173},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.308733195066452},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.26608842611312866},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.26319825649261475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09315213561058044},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08279925584793091}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8946106433868408},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6383534669876099},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5760533809661865},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5300689935684204},{"id":"https://openalex.org/C82006148","wikidata":"https://www.wikidata.org/wiki/Q913764","display_name":"Cauchy's integral formula","level":4,"score":0.5056414604187012},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.441513329744339},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4398479163646698},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42758530378341675},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3625979721546173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.308733195066452},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.26608842611312866},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.26319825649261475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09315213561058044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08279925584793091},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2012/634698","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/634698","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/634698.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:generic.eprints.org:38357","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401648","display_name":"Universiti Sains Malaysia Institutional Repository (Universiti Sains Malaysia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139322472","host_organization_name":"Universiti Sains Malaysia","host_organization_lineage":["https://openalex.org/I139322472"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:5be9189ddd754a869a67e8bd86b9a2dd","is_oa":true,"landing_page_url":"https://doaj.org/article/5be9189ddd754a869a67e8bd86b9a2dd","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/634698","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/634698","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/634698.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973803392.pdf","grobid_xml":"https://content.openalex.org/works/W1973803392.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W38816153","https://openalex.org/W1971947347","https://openalex.org/W2029063450","https://openalex.org/W2048320827","https://openalex.org/W2138249740"],"related_works":["https://openalex.org/W2600165055","https://openalex.org/W2485987855","https://openalex.org/W1998686718","https://openalex.org/W1032315593","https://openalex.org/W2950073196","https://openalex.org/W2110144359","https://openalex.org/W1973408980","https://openalex.org/W239288174","https://openalex.org/W4386543072","https://openalex.org/W3117797818"],"abstract_inverted_index":{"The":[0,26,55],"computation":[1,78],"of":[2,5,24,46,76,79,81],"the":[3,44,63,77,96],"roots":[4,45,80],"positive":[6,82],"definite":[7,83],"matrices":[8,84],"arises":[9,31],"in":[10,32,42],"nuclear":[11],"magnetic":[12],"resonance,":[13],"control":[14],"theory,":[15],"lattice":[16],"quantum":[17],"chromo-dynamics":[18],"(QCD),":[19],"and":[20],"several":[21],"other":[22],"areas":[23],"applications.":[25],"Cauchy":[27,56],"integral":[28,57,87],"theorem":[29],"which":[30],"complex":[33],"analysis":[34],"can":[35,58],"be":[36,59],"used":[37],"for":[38],"computing":[39],"f(A)":[40],",":[41,48],"particular":[43],"A":[47,50],"where":[49],"is":[51],"a":[52,73],"square":[53],"matrix.":[54],"approximated":[60],"by":[61,85],"using":[62],"trapezoid":[64],"rule.":[65],"In":[66],"this":[67],"paper,":[68],"we":[69],"aim":[70],"to":[71,94],"give":[72],"brief":[74],"overview":[75],"employing":[86],"representation.":[88],"Some":[89],"numerical":[90],"experiments":[91],"are":[92],"given":[93],"illustrate":[95],"theoretical":[97],"results.":[98]},"counts_by_year":[{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}