{"id":"https://openalex.org/W2147412345","doi":"https://doi.org/10.1007/s11075-012-9644-0","title":"Algorithm for min-range multiplication of affine forms","display_name":"Algorithm for min-range multiplication of affine forms","publication_year":2012,"publication_date":"2012-09-15","ids":{"openalex":"https://openalex.org/W2147412345","doi":"https://doi.org/10.1007/s11075-012-9644-0","mag":"2147412345"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-012-9644-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-012-9644-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9644-0.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9644-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030859159","display_name":"Iwona Skalna","orcid":"https://orcid.org/0000-0001-5707-7525"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Iwona Skalna","raw_affiliation_strings":["AGH University of Science and Technology, Krakow, Poland","AGH Univ. of Science and Technology, Krakow, Poland"],"affiliations":[{"raw_affiliation_string":"AGH University of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"AGH Univ. of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030859159"],"corresponding_institution_ids":["https://openalex.org/I686019"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16828035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"63","issue":"4","first_page":"601","last_page":"614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9973000288009644,"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/affine-transformation","display_name":"Affine transformation","score":0.8754515051841736},{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.849655032157898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7283786535263062},{"id":"https://openalex.org/keywords/affine-combination","display_name":"Affine combination","score":0.7159046530723572},{"id":"https://openalex.org/keywords/affine-hull","display_name":"Affine hull","score":0.6635322570800781},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6476700305938721},{"id":"https://openalex.org/keywords/affine-coordinate-system","display_name":"Affine coordinate system","score":0.6052379608154297},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6025326251983643},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.5878162384033203},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5510778427124023},{"id":"https://openalex.org/keywords/affine-shape-adaptation","display_name":"Affine shape adaptation","score":0.529920756816864},{"id":"https://openalex.org/keywords/affine-group","display_name":"Affine group","score":0.4419778287410736},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43427056074142456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42324361205101013},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.41774487495422363},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35103839635849},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.34412264823913574},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24283704161643982},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2320077121257782},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14978879690170288},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07713022828102112}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.8754515051841736},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.849655032157898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7283786535263062},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.7159046530723572},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.6635322570800781},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6476700305938721},{"id":"https://openalex.org/C95565831","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine coordinate system","level":4,"score":0.6052379608154297},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6025326251983643},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5878162384033203},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5510778427124023},{"id":"https://openalex.org/C18516315","wikidata":"https://www.wikidata.org/wiki/Q4688950","display_name":"Affine shape adaptation","level":4,"score":0.529920756816864},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.4419778287410736},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43427056074142456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42324361205101013},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.41774487495422363},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35103839635849},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.34412264823913574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24283704161643982},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2320077121257782},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14978879690170288},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07713022828102112},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-012-9644-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-012-9644-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9644-0.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-012-9644-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-012-9644-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-012-9644-0.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2147412345.pdf","grobid_xml":"https://content.openalex.org/works/W2147412345.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W33756405","https://openalex.org/W2016232724","https://openalex.org/W2052793175","https://openalex.org/W2055945485","https://openalex.org/W2131798279","https://openalex.org/W2162082792","https://openalex.org/W2273879208","https://openalex.org/W4233792602"],"related_works":["https://openalex.org/W2184784635","https://openalex.org/W2498386001","https://openalex.org/W2673935","https://openalex.org/W1510464305","https://openalex.org/W3021933917","https://openalex.org/W2964008969","https://openalex.org/W2077614002","https://openalex.org/W2038416447","https://openalex.org/W4300070731","https://openalex.org/W2147412345"],"abstract_inverted_index":{"Affine":[0],"arithmetic":[1],"produces":[2],"guaranteed":[3],"enclosures":[4],"for":[5,71,80,118,123,127],"computed":[6],"quantities,":[7],"taking":[8],"into":[9],"account":[10],"any":[11],"uncertainties":[12],"in":[13,32,39],"the":[14,54,82,89,108,112],"input":[15],"data":[16],"as":[17,19,45],"well":[18],"round-off":[20],"errors.":[21],"Elementary":[22],"operations":[23,36],"on":[24],"affine":[25,33,40,51,86,93],"forms":[26,94],"are":[27,103],"redefined":[28],"so":[29],"they":[30],"result":[31,37],"forms.":[34,41,52],"Affine-linear":[35],"straightforwardly":[38],"Non-linear":[42],"operators,":[43],"such":[44],"multiplication,":[46],"must":[47],"be":[48,68],"approximated":[49],"by":[50],"Choosing":[53],"appropriate":[55],"approximation":[56,87],"is":[57,63],"a":[58],"big":[59],"challenge.":[60],"The":[61],"reason":[62],"that":[64,95],"different":[65],"approximations":[66],"may":[67],"more":[69],"accurate":[70],"specific":[72],"purposes.":[73],"This":[74],"paper":[75],"presents":[76],"an":[77],"efficient":[78],"method":[79],"computing":[81],"minimum":[83],"range":[84],"(min-range)":[85],"of":[88,91,111,121,130],"product":[90],"arbitrary":[92],"do":[96],"not":[97],"contain":[98],"zero":[99],"properly.":[100],"Numerical":[101],"experiments":[102],"carried":[104],"out":[105],"to":[106],"demonstrate":[107],"essential":[109],"features":[110],"proposed":[113],"approach,":[114],"especially":[115],"its":[116],"usefulness":[117],"bounding":[119],"ranges":[120],"functions":[122],"global":[124],"optimisation":[125],"and":[126],"finding":[128],"roots":[129],"functions.":[131]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
