{"id":"https://openalex.org/W2054052206","doi":"https://doi.org/10.1090/s0025-5718-05-01796-5","title":"Computation of the Newton step for the even and odd characteristic polynomials of a symmetric positive definite Toeplitz matrix","display_name":"Computation of the Newton step for the even and odd characteristic polynomials of a symmetric positive definite Toeplitz matrix","publication_year":2005,"publication_date":"2005-12-01","ids":{"openalex":"https://openalex.org/W2054052206","doi":"https://doi.org/10.1090/s0025-5718-05-01796-5","mag":"2054052206"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01796-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01796-5","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01796-5/S0025-5718-05-01796-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01796-5/S0025-5718-05-01796-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081358638","display_name":"A. Melman","orcid":"https://orcid.org/0000-0001-6761-665X"},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Melman","raw_affiliation_strings":["Department of Applied Mathematics, School of Engineering, Santa Clara University, Santa Clara, California 95053"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Engineering, Santa Clara University, Santa Clara, California 95053","institution_ids":["https://openalex.org/I16269868"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081358638"],"corresponding_institution_ids":["https://openalex.org/I16269868"],"apc_list":null,"apc_paid":null,"fwci":0.6735,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71562275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"75","issue":"254","first_page":"817","last_page":"832"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory 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/T10792","display_name":"Matrix Theory 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/T11673","display_name":"Advanced Topics in Algebra","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12504","display_name":"Mathematics and Applications","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5646075010299683},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.4491342604160309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4063320755958557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32962435483932495},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12991511821746826}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5646075010299683},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.4491342604160309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4063320755958557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32962435483932495},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12991511821746826}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-05-01796-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01796-5","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01796-5/S0025-5718-05-01796-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.9510","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9510","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2006-75-254/S0025-5718-05-01796-5/S0025-5718-05-01796-5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01796-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01796-5","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-05-01796-5/S0025-5718-05-01796-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054052206.pdf","grobid_xml":"https://content.openalex.org/works/W2054052206.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W16220402","https://openalex.org/W1587896874","https://openalex.org/W1977519779","https://openalex.org/W1979923002","https://openalex.org/W1981745143","https://openalex.org/W2005926424","https://openalex.org/W2013351174","https://openalex.org/W2028458611","https://openalex.org/W2058367641","https://openalex.org/W2070760846","https://openalex.org/W2080178953","https://openalex.org/W2097690395","https://openalex.org/W2195864291","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2389462125","https://openalex.org/W2091997962","https://openalex.org/W151496359","https://openalex.org/W4220662591","https://openalex.org/W856465872","https://openalex.org/W1969863203","https://openalex.org/W1987843132","https://openalex.org/W1480644286","https://openalex.org/W2359223678"],"abstract_inverted_index":{"We":[0,34],"compute":[1],"the":[2,6,11,25,28,38],"Newton":[3],"step":[4],"for":[5,10],"characteristic":[7,15],"polynomial":[8],"and":[9,13],"even":[12],"odd":[14],"polynomials":[16],"of":[17,27,30],"a":[18,95],"symmetric":[19],"positive":[20],"definite":[21],"Toeplitz":[22],"matrix":[23],"as":[24],"reciprocal":[26],"trace":[29,44],"an":[31],"appropriate":[32],"matrix.":[33],"show":[35],"that,":[36],"after":[37],"Yule\u2013Walker":[39],"equations":[40],"are":[41],"solved,":[42],"this":[43],"can":[45],"be":[46],"computed":[47],"in":[48,87],"<inline-formula":[49,98],"content-type=\"math/mathml\">":[50,99],"<mml:math":[51,100],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[52,101],"alttext=\"script":[53,102],"upper":[54,103],"O":[55,104],"left-parenthesis":[56,105],"n":[57,106],"right-parenthesis\">":[58,108],"<mml:semantics>":[59,109],"<mml:mrow>":[60,110],"<mml:mrow":[61,63,111,113],"class=\"MJX-TeXAtom-ORD\">":[62,64,112,114],"<mml:mi":[65,115],"class=\"MJX-tex-caligraphic\"":[66,116],"mathvariant=\"script\">O</mml:mi>":[67,117],"</mml:mrow>":[68,69,75,118,119,128],"<mml:mo":[70,73,120,126],"stretchy=\"false\">(</mml:mo>":[71,121],"<mml:mi>n</mml:mi>":[72,123],"stretchy=\"false\">)</mml:mo>":[74,127],"<mml:annotation":[76,129],"encoding=\"application/x-tex\">{\\mathcal":[77,130],"O}(n)</mml:annotation>":[78],"</mml:semantics>":[79,132],"</mml:math>":[80,133],"</inline-formula>":[81,134],"additional":[82,135],"arithmetic":[83,136],"operations,":[84],"which":[85,92],"is":[86],"contrast":[88],"to":[89],"existing":[90],"methods,":[91],"rely":[93],"on":[94],"recursion,":[96],"requiring":[97],"squared":[107],"<mml:msup>":[122],"<mml:mn>2</mml:mn>":[124],"</mml:msup>":[125],"O}(n^2)</mml:annotation>":[131],"operations.":[137]},"counts_by_year":[],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}