{"id":"https://openalex.org/W2018419001","doi":"https://doi.org/10.1007/s006070050015","title":"A Sparse Matrix Arithmetic Based on $\\Cal H$ -Matrices. Part I: Introduction to ${\\Cal H}$ -Matrices","display_name":"A Sparse Matrix Arithmetic Based on $\\Cal H$ -Matrices. Part I: Introduction to ${\\Cal H}$ -Matrices","publication_year":1999,"publication_date":"1999-04-01","ids":{"openalex":"https://openalex.org/W2018419001","doi":"https://doi.org/10.1007/s006070050015","mag":"2018419001"},"language":"en","primary_location":{"id":"doi:10.1007/s006070050015","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s006070050015","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5084653980","display_name":"Wolfgang Hackbusch","orcid":"https://orcid.org/0000-0002-4801-6189"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"W. Hackbusch","raw_affiliation_strings":["Max Planck Institut Mathematik in den Naturwissenschaften Insel str. 22--26, D-04103 Leipzig, Germany, e-mail: wh@mis.mpg.de\n, , , , , , DE","Max Planck Institut, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institut Mathematik in den Naturwissenschaften Insel str. 22--26, D-04103 Leipzig, Germany, e-mail: wh@mis.mpg.de\n, , , , , , DE","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Max Planck Institut, Germany#TAB#","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084653980"],"corresponding_institution_ids":["https://openalex.org/I149899117","https://openalex.org/I4210091327"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":6.5834,"has_fulltext":false,"cited_by_count":1184,"citation_normalized_percentile":{"value":0.97856012,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"62","issue":"2","first_page":"89","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9975000023841858,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.758438229560852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7129204869270325},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6059775948524475},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.5669129490852356},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5025522708892822},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4844091534614563},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.47478005290031433},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.4619119465351105},{"id":"https://openalex.org/keywords/single-entry-matrix","display_name":"Single-entry matrix","score":0.4505676031112671},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4179072380065918},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3949345350265503},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36156243085861206},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3591907024383545},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.3223620057106018},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.29173895716667175},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.25890636444091797},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17475634813308716}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.758438229560852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7129204869270325},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6059775948524475},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.5669129490852356},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5025522708892822},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4844091534614563},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.47478005290031433},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.4619119465351105},{"id":"https://openalex.org/C1678238","wikidata":"https://www.wikidata.org/wiki/Q6787895","display_name":"Single-entry matrix","level":5,"score":0.4505676031112671},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4179072380065918},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3949345350265503},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36156243085861206},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3591907024383545},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.3223620057106018},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.29173895716667175},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.25890636444091797},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17475634813308716},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s006070050015","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s006070050015","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","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":6,"referenced_works":["https://openalex.org/W1513198935","https://openalex.org/W1569304948","https://openalex.org/W1602369757","https://openalex.org/W1974786074","https://openalex.org/W1989056711","https://openalex.org/W2005904620"],"related_works":["https://openalex.org/W2475184361","https://openalex.org/W2353337315","https://openalex.org/W2273176175","https://openalex.org/W2024093924","https://openalex.org/W2005347001","https://openalex.org/W4238100916","https://openalex.org/W2380177911","https://openalex.org/W2134388508","https://openalex.org/W2378018056","https://openalex.org/W2376122632"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":24},{"year":2025,"cited_by_count":31},{"year":2024,"cited_by_count":46},{"year":2023,"cited_by_count":42},{"year":2022,"cited_by_count":65},{"year":2021,"cited_by_count":54},{"year":2020,"cited_by_count":60},{"year":2019,"cited_by_count":82},{"year":2018,"cited_by_count":63},{"year":2017,"cited_by_count":80},{"year":2016,"cited_by_count":67},{"year":2015,"cited_by_count":70},{"year":2014,"cited_by_count":58},{"year":2013,"cited_by_count":48},{"year":2012,"cited_by_count":52}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2025-10-10T00:00:00"}
