{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:20:43Z","timestamp":1762323643791},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319022963"},{"type":"electronic","value":"9783319022970"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-319-02297-0_22","type":"book-chapter","created":{"date-parts":[[2013,8,14]],"date-time":"2013-08-14T11:37:38Z","timestamp":1376480258000},"page":"257-272","source":"Crossref","is-referenced-by-count":2,"title":["Extended QRGCD Algorithm"],"prefix":"10.1007","author":[{"given":"Kosaku","family":"Nagasaka","sequence":"first","affiliation":[]},{"given":"Takaaki","family":"Masui","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"22_CR1","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jsc.2012.06.003","volume":"50","author":"M.F. Roy","year":"2013","unstructured":"Roy, M.F., Sedjelmaci, S.M.: New fast euclidean algorithms. J. Symbolic Comput.\u00a050, 208\u2013226 (2013)","journal-title":"J. Symbolic Comput."},{"key":"22_CR2","volume-title":"Modern computer algebra","author":"J. Gathen von zur","year":"2003","unstructured":"von zur Gathen, J., Gerhard, J.: Modern computer algebra, 2nd edn. Cambridge University Press, Cambridge (2003)","edition":"2"},{"key":"22_CR3","unstructured":"Boito, P.: Structured Matrix Based Methods for Approximate GCD. Ph.D. Thesis. Department of Mathematics, University of Pisa, Italia (2007)"},{"key":"22_CR4","doi-asserted-by":"crossref","unstructured":"Zeng, Z.: The numerical greatest common divisor of univariate polynomials. In: Randomization, relaxation, and complexity in polynomial equation solving, Providence, RI. Contemp. Math. Amer. Math. Soc, vol.\u00a0556, pp. 187\u2013217 (2011)","DOI":"10.1090\/conm\/556\/11014"},{"key":"22_CR5","doi-asserted-by":"crossref","unstructured":"Kaltofen, E., Yang, Z., Zhi, L.: Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials. In: ISSAC 2006: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, pp. 169\u2013176 (2006)","DOI":"10.1145\/1145768.1145799"},{"key":"22_CR6","series-title":"Oper. Theory Adv. Appl","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/978-3-7643-8996-3_6","volume-title":"Numerical Methods for Structured Matrices and Applications","author":"D.A. Bini","year":"2010","unstructured":"Bini, D.A., Boito, P.: A fast algorithm for approximate polynomial GCD based on structured matrix computations. In: Numerical Methods for Structured Matrices and Applications. Oper. Theory Adv. Appl, vol.\u00a0199, pp. 155\u2013173. Birkh\u00e4user Verlag, Basel (2010)"},{"key":"22_CR7","doi-asserted-by":"crossref","unstructured":"Terui, A.: An iterative method for calculating approximate GCD of univariate polynomials. In: ISSAC 2009: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pp. 351\u2013358 (2009)","DOI":"10.1145\/1576702.1576750"},{"issue":"12","key":"22_CR8","doi-asserted-by":"publisher","first-page":"3394","DOI":"10.1109\/TSP.2004.837413","volume":"52","author":"R.M. Corless","year":"2004","unstructured":"Corless, R.M., Watt, S.M., Zhi, L.: QR factoring to compute the GCD of univariate approximate polynomials. IEEE Trans. Signal Process.\u00a052(12), 3394\u20133402 (2004)","journal-title":"IEEE Trans. Signal Process."},{"key":"22_CR9","doi-asserted-by":"publisher","first-page":"126","DOI":"10.2307\/2689124","volume":"42","author":"M.A. Laidacker","year":"1969","unstructured":"Laidacker, M.A.: Another theorem relating Sylvester\u2019s matrix and the greatest common divisor. Math. Mag.\u00a042, 126\u2013128 (1969)","journal-title":"Math. Mag."},{"key":"22_CR10","series-title":"Johns Hopkins Studies in the Mathematical Sciences","volume-title":"Matrix computations","author":"G.H. Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix computations, 3rd edn. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"issue":"4","key":"22_CR11","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1145\/500457.500458","volume":"33","author":"H.J. Stetter","year":"1999","unstructured":"Stetter, H.J.: The nearest polynomial with a given zero, and similar problems. SIGSAM Bull.\u00a033(4), 2\u20134 (1999)","journal-title":"SIGSAM Bull."},{"issue":"3","key":"22_CR12","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1145\/1113439.1113442","volume":"39","author":"N. Rezvani","year":"2005","unstructured":"Rezvani, N., Corless, R.M.: The nearest polynomial with a given zero, revisited. SIGSAM Bull.\u00a039(3), 73\u201379 (2005)","journal-title":"SIGSAM Bull."},{"key":"22_CR13","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1145\/321662.321665","volume":"18","author":"W.S. Brown","year":"1971","unstructured":"Brown, W.S., Traub, J.F.: On Euclid\u2019s algorithm and the theory of subresultants. J. Assoc. Comput. Mach.\u00a018, 505\u2013514 (1971)","journal-title":"J. Assoc. Comput. Mach."},{"issue":"3","key":"22_CR14","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.jsc.2006.09.003","volume":"42","author":"C. D\u2019Andrea","year":"2007","unstructured":"D\u2019Andrea, C., Hong, H., Krick, T., Szanto, A.: An elementary proof of Sylvester\u2019s double sums for subresultants. J. Symbolic Comput.\u00a042(3), 290\u2013297 (2007)","journal-title":"J. Symbolic Comput."},{"key":"22_CR15","doi-asserted-by":"crossref","unstructured":"Sasaki, T.: The subresultant and clusters of close roots. In: ISSAC 2003: Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 232\u2013239 (2003)","DOI":"10.1145\/860854.860902"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-02297-0_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T16:29:22Z","timestamp":1558024162000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-02297-0_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783319022963","9783319022970"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-02297-0_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}