{"id":"https://openalex.org/W4417040906","doi":"https://doi.org/10.1007/s10915-025-03150-2","title":"Spectral Analysis of $$\\tau $$-Preconditioners for Two-Level Toeplitz Systems with Applications in Nonlocal Diffusion Models","display_name":"Spectral Analysis of $$\\tau $$-Preconditioners for Two-Level Toeplitz Systems with Applications in Nonlocal Diffusion Models","publication_year":2025,"publication_date":"2025-12-05","ids":{"openalex":"https://openalex.org/W4417040906","doi":"https://doi.org/10.1007/s10915-025-03150-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-03150-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03150-2","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific 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/A5100758144","display_name":"Jiali Zhang","orcid":"https://orcid.org/0000-0003-3052-5329"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiali Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jiali Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiali Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103222846","display_name":"Tao Sun","orcid":"https://orcid.org/0009-0001-8065-0868"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Tao Sun","raw_affiliation_strings":["Department of Mathematics, University of Macau, Taipa, Macao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Macau, Taipa, Macao, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Haiwei Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Haiwei Sun","raw_affiliation_strings":["Department of Mathematics, University of Macau, Taipa, Macao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Macau, Taipa, Macao, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353054","display_name":"Jiwei Zhang","orcid":"https://orcid.org/0000-0003-3273-5581"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiwei Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100353054","display_name":"Jiwei Zhang","orcid":"https://orcid.org/0000-0003-3273-5581"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiwei Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100353054","https://openalex.org/A5100758144"],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31037757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"106","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.940500020980835,"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":0.940500020980835,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0203000009059906,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.002899999963119626,"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9002000093460083},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8747000098228455},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6762999892234802},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.597599983215332},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5658000111579895},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.4927000105381012},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4634000062942505},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.436599999666214},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.42289999127388},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.4174000024795532}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9002000093460083},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8747000098228455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8270999789237976},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6762999892234802},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5658000111579895},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49630001187324524},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.4927000105381012},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4763000011444092},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.436599999666214},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.42289999127388},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.4174000024795532},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3991999924182892},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.3698999881744385},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.3474000096321106},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.34130001068115234},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.3409000039100647},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.30410000681877136},{"id":"https://openalex.org/C131229623","wikidata":"https://www.wikidata.org/wiki/Q977297","display_name":"Trace class","level":3,"score":0.3019999861717224},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-03150-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03150-2","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W124312991","https://openalex.org/W147548410","https://openalex.org/W1504178724","https://openalex.org/W1591798773","https://openalex.org/W1814407173","https://openalex.org/W1970334228","https://openalex.org/W1973127220","https://openalex.org/W1988177606","https://openalex.org/W2004165073","https://openalex.org/W2006044588","https://openalex.org/W2009787868","https://openalex.org/W2011818561","https://openalex.org/W2012828992","https://openalex.org/W2043909302","https://openalex.org/W2044905083","https://openalex.org/W2057439610","https://openalex.org/W2060945009","https://openalex.org/W2070661544","https://openalex.org/W2073393685","https://openalex.org/W2078692435","https://openalex.org/W2082691187","https://openalex.org/W2083609718","https://openalex.org/W2084730628","https://openalex.org/W2086517326","https://openalex.org/W2093971242","https://openalex.org/W2097854981","https://openalex.org/W2098704097","https://openalex.org/W2112575052","https://openalex.org/W2139045013","https://openalex.org/W2162176806","https://openalex.org/W2169487141","https://openalex.org/W2326028551","https://openalex.org/W2795572994","https://openalex.org/W2903335383","https://openalex.org/W2957570416","https://openalex.org/W3126220907","https://openalex.org/W3163076066","https://openalex.org/W3195170616","https://openalex.org/W4230843528","https://openalex.org/W4239578497","https://openalex.org/W4242832160","https://openalex.org/W4244063180","https://openalex.org/W4252589316","https://openalex.org/W4283739939","https://openalex.org/W4285090095","https://openalex.org/W4286432971","https://openalex.org/W4303629077","https://openalex.org/W4382047254","https://openalex.org/W4386569047","https://openalex.org/W4387667149","https://openalex.org/W4404917887","https://openalex.org/W4407818556","https://openalex.org/W4415420917"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-12-05T00:00:00"}