{"id":"https://openalex.org/W2124740611","doi":"https://doi.org/10.1080/00207169908804797","title":"Enclosing the square root of a positive definite symmetric matrix","display_name":"Enclosing the square root of a positive definite symmetric matrix","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2124740611","doi":"https://doi.org/10.1080/00207169908804797","mag":"2124740611"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804797","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804797","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5101608029","display_name":"D. K. Gupta","orcid":"https://orcid.org/0009-0005-9776-7404"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"D. K. Gupta","raw_affiliation_strings":["Department of Mathematics , Indian Institute of Technology , Kharagpur, West-Bengal, 721302, India","Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, 721302, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Indian Institute of Technology , Kharagpur, West-Bengal, 721302, India","institution_ids":["https://openalex.org/I145894827"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, 721302, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076295200","display_name":"Chaitanya Kaul","orcid":"https://orcid.org/0000-0003-4893-6222"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"C. N. Kaul","raw_affiliation_strings":["Department of Mathematics , Indian Institute of Technology , Kharagpur, West-Bengal, 721302, India","Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, 721302, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Indian Institute of Technology , Kharagpur, West-Bengal, 721302, India","institution_ids":["https://openalex.org/I145894827"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, 721302, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101608029"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19171282,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"71","issue":"1","first_page":"105","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9824000000953674,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9811999797821045,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8535908460617065},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.8432992696762085},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.8419100046157837},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.7429574728012085},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.6018623113632202},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5701448321342468},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5657969117164612},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5609378814697266},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.5420932769775391},{"id":"https://openalex.org/keywords/square-root-of-a-2-by-2-matrix","display_name":"Square root of a 2 by 2 matrix","score":0.5414062142372131},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.47331130504608154},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4639688730239868},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44023096561431885},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34178051352500916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33085620403289795},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13185587525367737},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11076417565345764}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8535908460617065},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.8432992696762085},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.8419100046157837},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.7429574728012085},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6018623113632202},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5701448321342468},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5657969117164612},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5609378814697266},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.5420932769775391},{"id":"https://openalex.org/C14964150","wikidata":"https://www.wikidata.org/wiki/Q7582079","display_name":"Square root of a 2 by 2 matrix","level":5,"score":0.5414062142372131},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.47331130504608154},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4639688730239868},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44023096561431885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34178051352500916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33085620403289795},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13185587525367737},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11076417565345764},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804797","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804797","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":2,"referenced_works":["https://openalex.org/W132216871","https://openalex.org/W1975400766"],"related_works":["https://openalex.org/W2086824111","https://openalex.org/W2730547410","https://openalex.org/W2373948857","https://openalex.org/W2171562370","https://openalex.org/W2351159899","https://openalex.org/W2978783905","https://openalex.org/W3162079127","https://openalex.org/W2355201024","https://openalex.org/W3125742615","https://openalex.org/W2124740611"],"abstract_inverted_index":{"The":[0,44],"positive":[1,30],"definite":[2,31],"symmetric":[3,32],"square":[4,8,25,33,78],"matrices":[5],"have":[6],"unique":[7,77],"roots.":[9],"This":[10],"paper":[11],"describes":[12],"two":[13,68],"iterative":[14],"methods":[15,66],"using":[16],"the":[17,24,76],"concepts":[18],"of":[19,28,80],"interval":[20],"analysis":[21],"for":[22],"enclosing":[23],"root":[26,79],"S":[27,42],"a":[29,50],"matrix":[34],"A.":[35],"By":[36],"this,":[37],"we":[38],"mean":[39],"A":[40,81],"=":[41],"2.":[43],"second":[45],"method":[46],"is":[47],"tested":[48],"on":[49],"numerical":[51],"example":[52],"and":[53],"its":[54],"results":[55],"are":[56,60],"given.":[57],"Convergence":[58],"theorems":[59],"established":[61],"to":[62,75],"show":[63],"that":[64],"both":[65,73],"give":[67],"monotone":[69],"sequences":[70],"converging":[71],"from":[72],"sides":[74]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
