Nagasaka, Kosaku Relaxed NewtonSLRA for approximate GCD. (English) Zbl 07497960 Boulier, François (ed.) et al., Computer algebra in scientific computing. 23rd international workshop, CASC 2021, Sochi, Russia, September 13–17, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12865, 272-292 (2021). MSC: 68W30 PDFBibTeX XMLCite \textit{K. Nagasaka}, Lect. Notes Comput. Sci. 12865, 272--292 (2021; Zbl 07497960) Full Text: DOI
Nagasaka, Kosaku Toward the best algorithm for approximate GCD of univariate polynomials. (English) Zbl 1475.13050 J. Symb. Comput. 105, 4-27 (2021). MSC: 13P05 68W30 PDFBibTeX XMLCite \textit{K. Nagasaka}, J. Symb. Comput. 105, 4--27 (2021; Zbl 1475.13050) Full Text: DOI
Chi, Boming; Terui, Akira The GPGCD algorithm with the Bézout matrix. (English) Zbl 07635829 Boulier, François (ed.) et al., Computer algebra in scientific computing. 22nd international workshop, CASC 2020, Linz, Austria, September 14–18, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12291, 170-187 (2020). MSC: 68W30 PDFBibTeX XMLCite \textit{B. Chi} and \textit{A. Terui}, Lect. Notes Comput. Sci. 12291, 170--187 (2020; Zbl 07635829) Full Text: DOI
Nagasaka, Kosaku Approximate GCD by Bernstein basis, and its applications. (English) Zbl 07300094 Mantzaflaris, Angelos (ed.), Proceedings of the 45th international symposium on symbolic and algebraic computation, ISSAC ’20, Kalamata, Greece, July 20–23, 2020. New York, NY: Association for Computing Machinery (ACM). 372-379 (2020). MSC: 68W30 PDFBibTeX XMLCite \textit{K. Nagasaka}, in: Proceedings of the 45th international symposium on symbolic and algebraic computation, ISSAC '20, Kalamata, Greece, July 20--23, 2020. New York, NY: Association for Computing Machinery (ACM). 372--379 (2020; Zbl 07300094) Full Text: DOI
Lichtblau, Daniel Approximate polynomial GCD by approximate syzygies. (English) Zbl 1474.13053 Math. Comput. Sci. 13, No. 4, 517-532 (2019). MSC: 13P05 13P10 68W30 68W25 PDFBibTeX XMLCite \textit{D. Lichtblau}, Math. Comput. Sci. 13, No. 4, 517--532 (2019; Zbl 1474.13053) Full Text: DOI
Belhaj, Skander; Ben Kahla, Haithem; Dridi, Marwa; Moakher, Maher Blind image deconvolution via Hankel based method for computing the GCD of polynomials. (English) Zbl 1484.94005 Math. Comput. Simul. 144, 138-152 (2018). MSC: 94A08 68U10 PDFBibTeX XMLCite \textit{S. Belhaj} et al., Math. Comput. Simul. 144, 138--152 (2018; Zbl 1484.94005) Full Text: DOI
Vannet, Thomas; Kunihiro, Noboru Private information retrieval with preprocessing based on the approximate GCD problem. (English) Zbl 1396.68042 Dunkelman, Orr (ed.) et al., Selected areas in cryptography – SAC 2015. 22nd international conference, Sackville, NB, Canada, August 12–14, 2015. Revised selected papers. Cham: Springer (ISBN 978-3-319-31300-9/pbk; 978-3-319-31301-6/ebook). Lecture Notes in Computer Science 9566, 227-240 (2016). MSC: 68P25 68P20 94A60 PDFBibTeX XMLCite \textit{T. Vannet} and \textit{N. Kunihiro}, Lect. Notes Comput. Sci. 9566, 227--240 (2016; Zbl 1396.68042) Full Text: DOI
Terui, Akira GPGCD: an iterative method for calculating approximate GCD of univariate polynomials. (English) Zbl 1291.65162 Theor. Comput. Sci. 479, 127-149 (2013). MSC: 65H10 12Y05 12E05 68W30 PDFBibTeX XMLCite \textit{A. Terui}, Theor. Comput. Sci. 479, 127--149 (2013; Zbl 1291.65162) Full Text: DOI arXiv
Zhang, Zhenfei; Plantard, Thomas; Susilo, Willy On the CCA-1 security of somewhat homomorphic encryption over the integers. (English) Zbl 1291.94176 Ryan, Mark D. (ed.) et al., Information security practice and experience. 8th international conference, ISPEC 2012, Hangzhou, China, April 9–12, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-29100-5/pbk). Lecture Notes in Computer Science 7232, 353-368 (2012). MSC: 94A60 68P25 PDFBibTeX XMLCite \textit{Z. Zhang} et al., Lect. Notes Comput. Sci. 7232, 353--368 (2012; Zbl 1291.94176) Full Text: DOI
Elkadi, Mohamed; Galligo, André; Luu Ba Thang Approximate GCD of several univariate polynomials with small degree perturbations. (English) Zbl 1246.13040 J. Symb. Comput. 47, No. 4, 410-421 (2012). Reviewer: Carlos D’Andrea (Barcelona) MSC: 13P10 68W30 PDFBibTeX XMLCite \textit{M. Elkadi} et al., J. Symb. Comput. 47, No. 4, 410--421 (2012; Zbl 1246.13040) Full Text: DOI
Sanuki, Masaru Challenge to fast and stable computation of approximate univariate GCD, based on displacement structures. (English) Zbl 1346.68302 Moreno Maza, Marc (ed.), Proceedings of the 2011 international workshop on symbolic-numeric computation, SNC 2011, San Jose, CA, USA, June 7–11, 2011. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0515-0). 178-186 (2011). MSC: 68W30 12D05 12Y05 68Q25 PDFBibTeX XMLCite \textit{M. Sanuki}, in: Proceedings of the 2011 international workshop on symbolic-numeric computation, SNC 2011, San Jose, CA, USA, June 7--11, 2011. New York, NY: Association for Computing Machinery (ACM). 178--186 (2011; Zbl 1346.68302) Full Text: DOI
Corless, Robert M.; Postma, Erik; Stoutemyer, David R. GCD of multivariate approximate polynomials using beautification with the subtractive algorithm. (English) Zbl 1346.68279 Moreno Maza, Marc (ed.), Proceedings of the 2011 international workshop on symbolic-numeric computation, SNC 2011, San Jose, CA, USA, June 7–11, 2011. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0515-0). 153-154 (2011). MSC: 68W30 12D05 12Y05 13P05 65D99 PDFBibTeX XMLCite \textit{R. M. Corless} et al., in: Proceedings of the 2011 international workshop on symbolic-numeric computation, SNC 2011, San Jose, CA, USA, June 7--11, 2011. New York, NY: Association for Computing Machinery (ACM). 153--154 (2011; Zbl 1346.68279) Full Text: DOI
Nagasaka, Kosaku An improvement in the lattice construction process of approximate polynomial GCD over integers. (English) Zbl 1346.68296 Moreno Maza, Marc (ed.), Proceedings of the 2011 international workshop on symbolic-numeric computation, SNC 2011, San Jose, CA, USA, June 7–11, 2011. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0515-0). 63-64 (2011). MSC: 68W30 11C08 11Y16 68W25 PDFBibTeX XMLCite \textit{K. Nagasaka}, in: Proceedings of the 2011 international workshop on symbolic-numeric computation, SNC 2011, San Jose, CA, USA, June 7--11, 2011. New York, NY: Association for Computing Machinery (ACM). 63--64 (2011; Zbl 1346.68296) Full Text: DOI
Nagasaka, Kosaku Approximate polynomial GCD over integers. (English) Zbl 1248.11104 J. Symb. Comput. 46, No. 12, 1306-1317 (2011). MSC: 11Y16 68W20 65D99 11C08 PDFBibTeX XMLCite \textit{K. Nagasaka}, J. Symb. Comput. 46, No. 12, 1306--1317 (2011; Zbl 1248.11104) Full Text: DOI
Chèze, Guillaume; Galligo, André; Mourrain, Bernard; Yakoubsohn, Jean-Claude A subdivision method for computing nearest gcd with certification. (English) Zbl 1221.68297 Theor. Comput. Sci. 412, No. 35, 4493-4503 (2011). MSC: 68W30 12E05 65Y20 PDFBibTeX XMLCite \textit{G. Chèze} et al., Theor. Comput. Sci. 412, No. 35, 4493--4503 (2011; Zbl 1221.68297) Full Text: DOI
Li, Zijia; Yang, Zhengfeng; Zhi, Lihong Blind image deconvolution via fast approximate GCD. (English) Zbl 1321.68442 Watt, Stephen M. (ed.), Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25–28, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0150-3). 155-162 (2010). MSC: 68U10 65T50 68W30 PDFBibTeX XMLCite \textit{Z. Li} et al., in: Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25--28, 2010. New York, NY: Association for Computing Machinery (ACM). 155--162 (2010; Zbl 1321.68442) Full Text: DOI
von zur Gathen, Joachim; Mignotte, Maurice; Shparlinski, Igor E. Approximate polynomial GCD: small degree and small height perturbations. (English) Zbl 1248.11106 J. Symb. Comput. 45, No. 8, 879-886 (2010). MSC: 11Y16 68W20 65D99 11C08 PDFBibTeX XMLCite \textit{J. von zur Gathen} et al., J. Symb. Comput. 45, No. 8, 879--886 (2010; Zbl 1248.11106) Full Text: DOI
Chèze, Guillaume; Yakoubsohn, Jean-Claude; Galligo, André; Mourrain, Bernard Computing nearest gcd with certification. (English) Zbl 1356.68273 Kai, Hiroshi (ed.) et al., Proceedings of the 2009 workshop on symbolic-numeric computation, SNC 2009, Kyoto, Japan, August 3–5, 2009. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-664-9). 29-34 (2009). MSC: 68W30 12E05 68Q25 PDFBibTeX XMLCite \textit{G. Chèze} et al., in: Proceedings of the 2009 workshop on symbolic-numeric computation, SNC 2009, Kyoto, Japan, August 3--5, 2009. New York, NY: Association for Computing Machinery (ACM). 29--34 (2009; Zbl 1356.68273) Full Text: DOI
von zur Gathen, Joachim; Shparlinski, Igor E. Approximate polynomial GCD: small degree and small height perturbations. (English) Zbl 1136.68628 Laber, Eduardo Sany (ed.) et al., LATIN 2008: Theoretical informatics. 8th Latin American symposium, Búzios, Brazil, April 7–11, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-78772-3/pbk). Lecture Notes in Computer Science 4957, 276-283 (2008). MSC: 68W20 11Y16 65D99 11C08 PDFBibTeX XMLCite \textit{J. von zur Gathen} and \textit{I. E. Shparlinski}, Lect. Notes Comput. Sci. 4957, 276--283 (2008; Zbl 1136.68628) Full Text: DOI
Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials. (English) Zbl 1356.12011 Dumas, Jean-Guillaume (ed.), Proceedings of the 2006 international symposium on symbolic and algebraic computation, ISSAC 06, Genova, Italy, July 9–12, 2006. New York, NY: ACM Press (ISBN 1-59593-276-3). 169-176 (2006). MSC: 12Y05 12D05 68W30 PDFBibTeX XMLCite \textit{E. Kaltofen} et al., in: Proceedings of the 2006 international symposium on symbolic and algebraic computation, ISSAC 06, Genova, Italy, July 9--12, 2006. New York, NY: ACM Press. 169--176 (2006; Zbl 1356.12011) Full Text: DOI
Rupprecht, David An algorithm for computing certified approximate GCD of \(n\) univariate polynomials. (English) Zbl 0964.12007 J. Pure Appl. Algebra 139, No. 1-3, 255-284 (1999). Reviewer: V.Trevisan (Porto Alegre) MSC: 12Y05 65F30 15A18 65Y99 68W30 PDFBibTeX XMLCite \textit{D. Rupprecht}, J. Pure Appl. Algebra 139, No. 1--3, 255--284 (1999; Zbl 0964.12007) Full Text: DOI