{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:27:48Z","timestamp":1750220868231,"version":"3.41.0"},"reference-count":16,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T00:00:00Z","timestamp":1576540800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2019,12,17]]},"abstract":"<jats:p>\n            With the progress of algebraic computations on polynomials and matrices, we are paying more attention to approximate algebraic algorithms. Among approximate algebraic algorithms, those for calculating approximate greatest common divisor (GCD) consider a pair of given polynomials\n            <jats:italic>f<\/jats:italic>\n            and\n            <jats:italic>g<\/jats:italic>\n            that are relatively prime in general, and find f and g which are close to\n            <jats:italic>f<\/jats:italic>\n            and\n            <jats:italic>g<\/jats:italic>\n            , respectively, in the sense of polynomial norm, and have the GCD of certain degree. The algorithms can be classified into two categories: 1) for a given tolerance (magnitude) of ||\n            <jats:italic>f<\/jats:italic>\n            - f|| and ||\n            <jats:italic>g<\/jats:italic>\n            - g||, make the degree of approximate GCD as large as possible, and 2) for a given degree\n            <jats:italic>d<\/jats:italic>\n            , minimize the magnitude of ||\n            <jats:italic>f<\/jats:italic>\n            - f|| and ||\n            <jats:italic>g<\/jats:italic>\n            - g||.\n          <\/jats:p>","DOI":"10.1145\/3377006.3377010","type":"journal-article","created":{"date-parts":[[2019,12,18]],"date-time":"2019-12-18T13:21:11Z","timestamp":1576675271000},"page":"99-102","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["The GPGCD algorithm with the B\u00e9zout matrix"],"prefix":"10.1145","volume":"53","author":[{"given":"Boming","family":"Chi","sequence":"first","affiliation":[{"name":"University of Tsukuba, Tsukuba, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akira","family":"Terui","sequence":"additional","affiliation":[{"name":"University of Tsukuba, Tsukuba, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,12,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2001.0462"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/220346.220371"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2004.837413"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2002.0542"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(97)00013-3"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1145768.1145799"},{"key":"e_1_2_1_7_1","first-page":"69","volume-title":"Structured low rank approximation of a Sylvester matrix","author":"Kaltofen E.","year":"2007","unstructured":"E. Kaltofen , Z. Yang , and L. Zhi . Structured low rank approximation of a Sylvester matrix . In D. Wang and L. Zhi, editors, Symbolic-Numeric Computation, Trends in Mathematics, pages 69 -- 83 . Birkh\u00e3user , 2007 . E. Kaltofen, Z. Yang, and L. Zhi. Structured low rank approximation of a Sylvester matrix. In D. Wang and L. Zhi, editors, Symbolic-Numeric Computation, Trends in Mathematics, pages 69--83. Birkh\u00e3user, 2007."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/0109044"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-015-9256-x"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11786-007-0014-6"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934495"},{"key":"e_1_2_1_12_1","unstructured":"A. Terui. A dataset for the GPGCD algorithm. https:\/\/github.com\/atelieraterui\/tcs-snc2011-data.  A. Terui. A dataset for the GPGCD algorithm. https:\/\/github.com\/atelieraterui\/tcs-snc2011-data."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1576702.1576750"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.10.023"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/78.875462"},{"key":"e_1_2_1_16_1","volume-title":"Six Asian Symposium on Computer Mathematics (ASCM 2003","volume":"10","author":"Zhi L.","year":"2003","unstructured":"L. Zhi . Displacement structure in computing approximate GCD of univariate polynomials. In Computer mathematics: Proc . Six Asian Symposium on Computer Mathematics (ASCM 2003 ), volume 10 of Lecture Notes Ser. Comput., pages 288--298. World Sci. Publ., River Edge, NJ , 2003 . L. Zhi. Displacement structure in computing approximate GCD of univariate polynomials. In Computer mathematics: Proc. Six Asian Symposium on Computer Mathematics (ASCM 2003), volume 10 of Lecture Notes Ser. Comput., pages 288--298. World Sci. Publ., River Edge, NJ, 2003."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3377006.3377010","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3377006.3377010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:23:49Z","timestamp":1750202629000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3377006.3377010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,17]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,12,17]]}},"alternative-id":["10.1145\/3377006.3377010"],"URL":"https:\/\/doi.org\/10.1145\/3377006.3377010","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2019,12,17]]},"assertion":[{"value":"2019-12-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}