{"id":"https://openalex.org/W2057542391","doi":"https://doi.org/10.1080/17445760601122084","title":"A Hilbert-order multiplication scheme for unstructured sparse matrices","display_name":"A Hilbert-order multiplication scheme for unstructured sparse matrices","publication_year":2007,"publication_date":"2007-06-14","ids":{"openalex":"https://openalex.org/W2057542391","doi":"https://doi.org/10.1080/17445760601122084","mag":"2057542391"},"language":"en","primary_location":{"id":"doi:10.1080/17445760601122084","is_oa":false,"landing_page_url":"https://doi.org/10.1080/17445760601122084","pdf_url":null,"source":{"id":"https://openalex.org/S85375271","display_name":"International Journal of Parallel Emergent and Distributed Systems","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192","1744-5760","1744-5779"],"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 Parallel, Emergent and Distributed Systems","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/A5078920331","display_name":"Gundolf Haase","orcid":"https://orcid.org/0000-0002-3439-6117"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Gundolf Haase","raw_affiliation_strings":["Institute for Mathematics and Scientific Computing, Karl-Franzens University Graz, Heinrichstr. 36, A-8010, Graz, Austria","Institute for Mathematics and Scientific Computing, Karl\u2013Franzens University Graz , Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and Scientific Computing, Karl-Franzens University Graz, Heinrichstr. 36, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Institute for Mathematics and Scientific Computing, Karl\u2013Franzens University Graz , Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090967117","display_name":"Manfred Liebmann","orcid":null},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Manfred Liebmann","raw_affiliation_strings":["Institute for Mathematics and Scientific Computing, Karl-Franzens University Graz, Heinrichstr. 36, A-8010, Graz, Austria","Institute for Mathematics and Scientific Computing, Karl\u2013Franzens University Graz , Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and Scientific Computing, Karl-Franzens University Graz, Heinrichstr. 36, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Institute for Mathematics and Scientific Computing, Karl\u2013Franzens University Graz , Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012616951","display_name":"Gernot Plank","orcid":"https://orcid.org/0000-0002-7380-6908"},"institutions":[{"id":"https://openalex.org/I202276237","display_name":"Medical University of Graz","ror":"https://ror.org/02n0bts35","country_code":"AT","type":"education","lineage":["https://openalex.org/I202276237"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Gernot Plank","raw_affiliation_strings":["Institute of Biophysic, Medical University of Graz, Harrachgasse 21/4, A-8010, Graz, Austria","Institute of Biophysic, Medical University of Graz, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Biophysic, Medical University of Graz, Harrachgasse 21/4, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I202276237"]},{"raw_affiliation_string":"Institute of Biophysic, Medical University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I202276237"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078920331"],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":null,"apc_paid":null,"fwci":0.4169,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.7654321,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"22","issue":"4","first_page":"213","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7579425573348999},{"id":"https://openalex.org/keywords/hilbert-curve","display_name":"Hilbert curve","score":0.7562369704246521},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5630370378494263},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5493265986442566},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5313076972961426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4892582893371582},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.45405346155166626},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4219009280204773},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4140809178352356},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.406685471534729},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.393609881401062},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36893734335899353},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1970447599887848},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19035464525222778},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09265464544296265},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.061392784118652344}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7579425573348999},{"id":"https://openalex.org/C2781142347","wikidata":"https://www.wikidata.org/wiki/Q1366592","display_name":"Hilbert curve","level":2,"score":0.7562369704246521},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5630370378494263},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5493265986442566},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5313076972961426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4892582893371582},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.45405346155166626},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4219009280204773},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4140809178352356},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.406685471534729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.393609881401062},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36893734335899353},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1970447599887848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19035464525222778},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09265464544296265},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.061392784118652344},{"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/17445760601122084","is_oa":false,"landing_page_url":"https://doi.org/10.1080/17445760601122084","pdf_url":null,"source":{"id":"https://openalex.org/S85375271","display_name":"International Journal of Parallel Emergent and Distributed Systems","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192","1744-5760","1744-5779"],"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 Parallel, Emergent and Distributed Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.641.939","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.641.939","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.numa.uni-linz.ac.at/publications/List/2005/IMA03-05.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":15,"referenced_works":["https://openalex.org/W171803481","https://openalex.org/W579331379","https://openalex.org/W641349311","https://openalex.org/W1530872699","https://openalex.org/W1531802798","https://openalex.org/W1575450360","https://openalex.org/W1964639877","https://openalex.org/W1980308665","https://openalex.org/W1997542937","https://openalex.org/W2056345907","https://openalex.org/W2117562284","https://openalex.org/W2158544504","https://openalex.org/W2163370224","https://openalex.org/W2769954494","https://openalex.org/W4240774490"],"related_works":["https://openalex.org/W4287593139","https://openalex.org/W3099313426","https://openalex.org/W1506547947","https://openalex.org/W2086146848","https://openalex.org/W4206811032","https://openalex.org/W2995605830","https://openalex.org/W4239424132","https://openalex.org/W2596457687","https://openalex.org/W3212757063","https://openalex.org/W2086123442"],"abstract_inverted_index":{"We":[0],"investigate":[1],"a":[2],"new":[3],"storage":[4,27,37],"format":[5,29,42,46],"for":[6,51],"unstructured":[7],"sparse":[8],"matrices":[9],"based":[10],"on":[11],"the":[12,22,25,33,44],"space-filling":[13],"Hilbert":[14],"curve.":[15],"Numerical":[16],"tests":[17],"with":[18,54],"matrix-vector":[19,52],"multiplication":[20],"show":[21],"potential":[23],"of":[24],"fractal":[26],"(FS)":[28],"in":[30],"comparison":[31],"to":[32,49],"traditional":[34],"compressed":[35],"row":[36],"(CRS)":[38],"format.":[39],"The":[40],"FS":[41],"outperforms":[43],"CRS":[45],"by":[47],"up":[48],"50%":[50],"multiplications":[53],"multiple":[55],"right":[56],"hand":[57],"sides.":[58]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":17}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
