{"id":"https://openalex.org/W2078488968","doi":"https://doi.org/10.1137/0614049","title":"Mixed, Componentwise, and Structured Condition Numbers","display_name":"Mixed, Componentwise, and Structured Condition Numbers","publication_year":1993,"publication_date":"1993-07-01","ids":{"openalex":"https://openalex.org/W2078488968","doi":"https://doi.org/10.1137/0614049","mag":"2078488968"},"language":"en","primary_location":{"id":"doi:10.1137/0614049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614049","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5024554995","display_name":"Israel Gohberg","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"I. Gohberg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073207382","display_name":"I. Koltracht","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. Koltracht","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024554995"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0507,"has_fulltext":false,"cited_by_count":129,"citation_normalized_percentile":{"value":0.91789897,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"688","last_page":"704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.898604154586792},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8813387155532837},{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.779052734375},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4914909601211548},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4639555811882019},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4609108567237854},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.42902445793151855},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40364283323287964},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3233442008495331},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3131799101829529},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.098560631275177}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.898604154586792},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8813387155532837},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.779052734375},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4914909601211548},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4639555811882019},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4609108567237854},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.42902445793151855},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40364283323287964},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3233442008495331},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3131799101829529},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.098560631275177},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0614049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614049","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1514966789","https://openalex.org/W1617761643","https://openalex.org/W1963628831","https://openalex.org/W2021311647","https://openalex.org/W2030638350","https://openalex.org/W2038336192","https://openalex.org/W2060854423","https://openalex.org/W2077166865","https://openalex.org/W2102140633","https://openalex.org/W2116208340","https://openalex.org/W2124526559","https://openalex.org/W2129256515","https://openalex.org/W2166036437","https://openalex.org/W2752908210","https://openalex.org/W4244681853","https://openalex.org/W4249703615","https://openalex.org/W4300421229","https://openalex.org/W4302769929"],"related_works":["https://openalex.org/W2394313973","https://openalex.org/W1258664604","https://openalex.org/W4285223790","https://openalex.org/W2952052090","https://openalex.org/W4293585078","https://openalex.org/W2389636997","https://openalex.org/W2349018871","https://openalex.org/W2080915594","https://openalex.org/W2037847497","https://openalex.org/W2016131521"],"abstract_inverted_index":{"Mixed,":[0],"componentwise,":[1],"and":[2,28],"structured":[3],"condition":[4,24],"numbers":[5,25],"for":[6,19],"continuous":[7],"maps":[8],"in":[9],"finite-dimensional":[10],"spaces":[11],"are":[12,26,40],"introduced.":[13],"For":[14],"differentiable":[15],"maps,":[16],"convenient":[17],"formulas":[18],"the":[20,31],"estimation":[21],"of":[22,33],"such":[23],"given":[27],"illustrated":[29],"on":[30],"example":[32],"Toeplitz":[34],"matrices.":[35],"Applications":[36],"to":[37],"Vandermonde":[38],"matrices":[39],"also":[41],"presented.":[42]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
