{"id":"https://openalex.org/W1964189189","doi":"https://doi.org/10.1137/060669176","title":"Symmetric Permutations for I-matrices to Delay and Avoid Small Pivots During Factorization","display_name":"Symmetric Permutations for I-matrices to Delay and Avoid Small Pivots During Factorization","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1964189189","doi":"https://doi.org/10.1137/060669176","mag":"1964189189"},"language":"en","primary_location":{"id":"doi:10.1137/060669176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060669176","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5445/ir/1000005031","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026125584","display_name":"Jan Mayer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jan Mayer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026125584"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8811,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.900725,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"30","issue":"2","first_page":"982","last_page":"996"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8589648008346558},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.7518713474273682},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6566773653030396},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6518064737319946},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5683285593986511},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.528369665145874},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.5193803906440735},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.5051591992378235},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.49455878138542175},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.4668966233730316},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.44969800114631653},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4484083354473114},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41616880893707275},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4137047529220581},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.3958870768547058},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3950765132904053},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34371793270111084},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.343569278717041},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3129822015762329},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25296124815940857},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15462452173233032},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.14483946561813354},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11006966233253479}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8589648008346558},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.7518713474273682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6566773653030396},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6518064737319946},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5683285593986511},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.528369665145874},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.5193803906440735},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.5051591992378235},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.49455878138542175},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.4668966233730316},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.44969800114631653},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4484083354473114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41616880893707275},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4137047529220581},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3958870768547058},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3950765132904053},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34371793270111084},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.343569278717041},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3129822015762329},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25296124815940857},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15462452173233032},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.14483946561813354},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11006966233253479},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":6,"locations":[{"id":"doi:10.1137/060669176","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060669176","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000005031","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000005031","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"doc-type:report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.308.8064","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.8064","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.kit.edu/iwrmm/seite/preprints/media/iwrmm-preprint-06-08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.663.9518","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.663.9518","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://digbib.ubka.uni-karlsruhe.de/volltexte/documents/246126/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.93.5628","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.5628","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.uni-karlsruhe.de/iwrmm/seite/preprints/media/preprint nr. 06-08.pdf","raw_type":"text"},{"id":"doi:10.5445/ir/1000005031","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000005031","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"report"}],"best_oa_location":{"id":"doi:10.5445/ir/1000005031","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000005031","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"report"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W23203733","https://openalex.org/W1506342804","https://openalex.org/W1581078542","https://openalex.org/W1965394225","https://openalex.org/W1974336758","https://openalex.org/W1986559128","https://openalex.org/W2003105834","https://openalex.org/W2017431061","https://openalex.org/W2029041499","https://openalex.org/W2040733945","https://openalex.org/W2041785146","https://openalex.org/W2055987340","https://openalex.org/W2069849438","https://openalex.org/W2070232376","https://openalex.org/W2073555064","https://openalex.org/W2150003608"],"related_works":["https://openalex.org/W1543309964","https://openalex.org/W2029041499","https://openalex.org/W3010195088","https://openalex.org/W2023930998","https://openalex.org/W2055020807","https://openalex.org/W1991995462","https://openalex.org/W2150003608","https://openalex.org/W2548114753","https://openalex.org/W2911589527","https://openalex.org/W1964189189"],"abstract_inverted_index":{"In":[0,77],"this":[1,78],"article,":[2,79],"we":[3,80],"present":[4],"several":[5],"new":[6],"permutations":[7],"for":[8,14,92,143],"I-matrices":[9],"making":[10],"these":[11,120],"more":[12,62,90],"suitable":[13,91],"incomplete":[15,94,107,136],"LU-factorization":[16,95,108],"preconditioners":[17],"used":[18],"in":[19,155],"solving":[20],"linear":[21],"systems":[22],"by":[23,32,70],"iterative":[24],"methods.":[25],"A":[26],"general":[27],"matrix":[28,47,89],"can":[29],"be":[30],"transformed":[31],"row":[33,38],"permutation":[34,73],"as":[35,37],"well":[36],"and":[39,56,68,133],"columns":[40,69],"scaling":[41],"into":[42],"an":[43,93,106],"I-matrix,":[44],"i.e.,":[45],"a":[46,103,139],"having":[48],"elements":[49,57],"of":[50,58,60,113,124],"modulus":[51,59],"1":[52,64],"on":[53],"the":[54,71,87,98,128,134,156],"diagonal":[55],"no":[61],"than":[63,97],"elsewhere.":[65],"Reordering":[66],"rows":[67],"same":[72],"clearly":[74],"preserves":[75],"I-matrices.":[76],"consider":[81],"such":[82],"reordering":[83],"techniques":[84],"which":[85],"make":[86],"permuted":[88],"preconditioner":[96,109],"original":[99],"I-matrix.":[100],"We":[101],"use":[102],"multilevel":[104,135],"ILUC,":[105],"using":[110],"Crout's":[111],"implementation":[112],"Gaussian":[114],"elimination":[115],"without":[116],"pivoting":[117],"to":[118],"test":[119],"reorderings.":[121],"The":[122,148],"combination":[123],"I-matrix":[125],"preprocessing":[126],"with":[127],"various":[129],"algorithms":[130],"presented":[131],"here":[132],"LU-factorizations":[137],"forms":[138],"powerful":[140],"preconditioning":[141],"method":[142],"unsymmetric,":[144],"highly":[145],"indefinite":[146],"problems.":[147],"C++":[149],"code":[150],"has":[151],"been":[152],"made":[153],"available":[154],"software":[157],"package":[158],"ILU++.":[159]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}