{"id":"https://openalex.org/W3118879558","doi":"https://doi.org/10.1137/20m1348595","title":"AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models","display_name":"AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3118879558","doi":"https://doi.org/10.1137/20m1348595","mag":"3118879558"},"language":"en","primary_location":{"id":"doi:10.1137/20m1348595","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1348595","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2408.00559","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041586461","display_name":"Jos\u00e9 Germ\u00e1n L\u00f3pez-Salas","orcid":"https://orcid.org/0000-0002-4533-0754"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. G. L\u00f3pez-Salas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025703808","display_name":"S. P\u00e9rez-Rodr\u00edguez","orcid":"https://orcid.org/0000-0002-3902-8313"},"institutions":[{"id":"https://openalex.org/I158438070","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25","country_code":"ES","type":"education","lineage":["https://openalex.org/I158438070"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. P\u00e9rez-Rodr\u00edguez","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38208, La Laguna, Tenerife, Canary Islands, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38208, La Laguna, Tenerife, Canary Islands, Spain","institution_ids":["https://openalex.org/I158438070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063346914","display_name":"Carlos V\u00e1zquez","orcid":"https://orcid.org/0000-0001-6591-2252"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"C. V\u00e1zquez","raw_affiliation_strings":["Department of Mathematics and CITIC, Universidade da Coru\u00f1a, Campus de Elvi\u00f1a s/n, 15071 -A Coru\u00f1a, Spain"],"raw_orcid":"https://orcid.org/0000-0001-6591-2252","affiliations":[{"raw_affiliation_string":"Department of Mathematics and CITIC, Universidade da Coru\u00f1a, Campus de Elvi\u00f1a s/n, 15071 -A Coru\u00f1a, Spain","institution_ids":["https://openalex.org/I11019714"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7706,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80848914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"43","issue":"1","first_page":"B30","last_page":"B54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9983999729156494,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/mathematics","display_name":"Mathematics","score":0.540088951587677},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5205848813056946},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5105463266372681},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.4782339930534363},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4609736502170563},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.44331467151641846},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4262693524360657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42056334018707275},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4171901047229767},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4149949252605438},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4149731695652008},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4141899049282074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40138623118400574},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3461347818374634},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17619779706001282},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1215636134147644},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10278439521789551}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.540088951587677},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5205848813056946},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5105463266372681},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4782339930534363},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4609736502170563},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44331467151641846},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4262693524360657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42056334018707275},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4171901047229767},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4149949252605438},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4149731695652008},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4141899049282074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40138623118400574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3461347818374634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17619779706001282},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1215636134147644},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10278439521789551},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1348595","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1348595","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:arXiv.org:2408.00559","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2408.00559","pdf_url":"https://arxiv.org/pdf/2408.00559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ruc.udc.es:2183/38185","is_oa":true,"landing_page_url":"http://hdl.handle.net/2183/38185","pdf_url":null,"source":{"id":"https://openalex.org/S4306402204","display_name":"RUC (Universidade Da Coru\u00f1a)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11019714","host_organization_name":"Universidade da Coru\u00f1a","host_organization_lineage":["https://openalex.org/I11019714"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:14538035","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20M1348595","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 43(1), B30-B54, (2021-01-05)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2408.00559","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2408.00559","pdf_url":"https://arxiv.org/pdf/2408.00559","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1888088267","display_name":null,"funder_award_id":"2014-2020\u2019","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G1933851018","display_name":null,"funder_award_id":"ED431G 2019/01","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G1953887145","display_name":null,"funder_award_id":"2014\u20102020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3199046289","display_name":null,"funder_award_id":"ED431G 2019/01","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3876637791","display_name":null,"funder_award_id":"ED431G","funder_id":"https://openalex.org/F4320326655","funder_display_name":"Xunta de Galicia"},{"id":"https://openalex.org/G6425714947","display_name":null,"funder_award_id":"ED431C 2018/033","funder_id":"https://openalex.org/F4320326655","funder_display_name":"Xunta de Galicia"},{"id":"https://openalex.org/G7224627388","display_name":null,"funder_award_id":"ED431","funder_id":"https://openalex.org/F4320326655","funder_display_name":"Xunta de Galicia"},{"id":"https://openalex.org/G726424357","display_name":null,"funder_award_id":"ED431G 2019/01","funder_id":"https://openalex.org/F4320326655","funder_display_name":"Xunta de Galicia"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320326655","display_name":"Xunta de Galicia","ror":"https://ror.org/0181xnw06"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3118879558.pdf","grobid_xml":"https://content.openalex.org/works/W3118879558.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W3331290","https://openalex.org/W1987020393","https://openalex.org/W2010210658","https://openalex.org/W2010452605","https://openalex.org/W2028789893","https://openalex.org/W2031336791","https://openalex.org/W2035093540","https://openalex.org/W2038772236","https://openalex.org/W2047725321","https://openalex.org/W2077681241","https://openalex.org/W2090615286","https://openalex.org/W2108785452","https://openalex.org/W2117842679","https://openalex.org/W2126408836","https://openalex.org/W2157899933","https://openalex.org/W2162277293","https://openalex.org/W2168555104","https://openalex.org/W2184962859","https://openalex.org/W2186711713","https://openalex.org/W2423780729","https://openalex.org/W2521641892","https://openalex.org/W2526347135","https://openalex.org/W2709506240","https://openalex.org/W2755560623","https://openalex.org/W2781240167","https://openalex.org/W2806737128","https://openalex.org/W2891717620","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W4229577910","https://openalex.org/W2800324324","https://openalex.org/W2640255794","https://openalex.org/W2743060302","https://openalex.org/W2054089597","https://openalex.org/W2791597622","https://openalex.org/W2117656216","https://openalex.org/W2026707481","https://openalex.org/W2626358056","https://openalex.org/W1480631731"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,27],"mainly":[4],"develop":[5],"a":[6,12,34,78,85,106,169,175],"new":[7,133],"numerical":[8],"methodology":[9],"to":[10,33,142,147,173],"solve":[11],"PDE":[13,94],"model":[14],"recently":[15],"proposed":[16],"in":[17,48,57,98,158,177],"the":[18,49,66,69,74,82,93,101,125,130,144,148,166,178,181],"literature":[19],"for":[20,77],"pricing":[21],"interest":[22],"rate":[23],"derivatives.":[24,54],"More":[25],"precisely,":[26],"use":[28,102],"high-order-in-time":[29],"AMFR-W-methods,":[30],"which":[31],"belong":[32],"class":[35],"of":[36,51,68,84,88,103,127,132,150,168,180],"W-methods":[37],"based":[38],"on":[39],"approximate":[40],"matrix":[41],"factorization":[42],"(AMF)":[43],"and":[44,123],"are":[45],"especially":[46,157],"suitable":[47],"presence":[50,149],"mixed":[52],"spatial":[53],"High-order":[55],"convergence":[56],"time":[58,61,76],"allows":[59],"larger":[60],"steps,":[62],"which,":[63],"combined":[64],"with":[65,105,120],"splitting":[67],"involved":[70],"operators,":[71],"highly":[72],"reduces":[73],"computational":[75],"given":[79],"accuracy.":[80],"Moreover,":[81],"consideration":[83,131],"large":[86],"number":[87],"underlying":[89],"forward":[90],"rates":[91],"makes":[92],"problem":[95],"high":[96],"dimensional":[97],"space,":[99],"so":[100],"AMFR-W-methods":[104],"sparse":[107],"grid":[108],"combination":[109,171,183],"technique":[110,172],"represents":[111],"another":[112,139],"innovative":[113],"aspect,":[114],"making":[115],"AMFR-W":[116],"more":[117],"efficient":[118],"than":[119],"full":[121],"grids":[122],"opening":[124],"possibility":[126],"parallelization.":[128],"Also,":[129],"homogeneous":[134],"Neumann":[135,162],"boundary":[136,151,163],"conditions":[137,164],"provides":[138],"original":[140],"feature":[141],"avoid":[143],"difficulties":[145],"associated":[146],"layers":[152],"when":[153],"using":[154],"Dirichlet":[155],"ones,":[156],"advection-dominated":[159],"regimes.":[160],"These":[161],"motivate":[165],"introduction":[167],"modified":[170],"overcome":[174],"decrease":[176],"accuracy":[179],"standard":[182],"technique.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2021-01-18T00:00:00"}