Nagasaka, Kosaku SLRA interpolation for approximate GCD of several multivariate polynomials. (English) Zbl 07760793 Dickenstein, Alicia (ed.) et al., Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24–27, 2023. New York, NY: Association for Computing Machinery (ACM). 470-479 (2023). MSC: 68W30 PDFBibTeX XMLCite \textit{K. Nagasaka}, in: Proceedings of the 48th international symposium on symbolic and algebraic computation, ISSAC, Tromsø, Norway, July 24--27, 2023. New York, NY: Association for Computing Machinery (ACM). 470--479 (2023; Zbl 07760793) Full Text: DOI
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
Pérez-Díaz, Sonia; Shen, Li-Yong Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis. (English) Zbl 1465.14056 Comput. Aided Geom. Des. 84, Article ID 101957, 14 p. (2021). Reviewer: Franz Winkler (Linz) MSC: 14Q05 65D18 68U07 PDFBibTeX XMLCite \textit{S. Pérez-Díaz} and \textit{L.-Y. Shen}, Comput. Aided Geom. Des. 84, Article ID 101957, 14 p. (2021; Zbl 1465.14056) 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
Duan, Qihong; Liu, Junrong Filtering and smoothing formulas of AR \((p)\)-modulated Poisson processes. (English) Zbl 07553267 Commun. Stat., Simulation Comput. 49, No. 6, 1575-1591 (2020). MSC: 62-XX PDFBibTeX XMLCite \textit{Q. Duan} and \textit{J. Liu}, Commun. Stat., Simulation Comput. 49, No. 6, 1575--1591 (2020; Zbl 07553267) Full Text: DOI
Bourne, Martin; Winkler, Joab; Su, Yi The computation of multiple roots of a Bernstein basis polynomial. (English) Zbl 1431.65064 SIAM J. Sci. Comput. 42, No. 1, A452-A476 (2020). MSC: 65H04 12-08 PDFBibTeX XMLCite \textit{M. Bourne} et al., SIAM J. Sci. Comput. 42, No. 1, A452--A476 (2020; Zbl 1431.65064) Full Text: DOI
Xu, Jun; Sarkar, Santanu; Hu, Lei Revisiting approximate polynomial common divisor problem and noisy multipolynomial reconstruction. (English) Zbl 1456.94119 Hao, Feng (ed.) et al., Progress in cryptology – INDOCRYPT 2019. 20th international conference on cryptology in India, Hyderabad, India, December 15–18, 2019. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11898, 398-411 (2019). MSC: 94A60 11A05 11J70 PDFBibTeX XMLCite \textit{J. Xu} et al., Lect. Notes Comput. Sci. 11898, 398--411 (2019; Zbl 1456.94119) Full Text: DOI
Li, Zijia; Scharler, Daniel F.; Schröcker, Hans-Peter Factorization results for left polynomials in some associative real algebras: state of the art, applications, and open questions. (English) Zbl 1425.12001 J. Comput. Appl. Math. 349, 508-522 (2019). Reviewer: Eckhard Hitzer (Tokyo) MSC: 12D05 15A66 16S36 30C15 70B15 PDFBibTeX XMLCite \textit{Z. Li} et al., J. Comput. Appl. Math. 349, 508--522 (2019; Zbl 1425.12001) Full Text: DOI arXiv
Li, Zijia; Schicho, Josef; Schröcker, Hans-Peter Kempe’s universality theorem for rational space curves. (English) Zbl 1430.70006 Found. Comput. Math. 18, No. 2, 509-536 (2018). MSC: 70B05 14H50 65D17 68U07 PDFBibTeX XMLCite \textit{Z. Li} et al., Found. Comput. Math. 18, No. 2, 509--536 (2018; Zbl 1430.70006) Full Text: DOI arXiv
Jia, Xiaohong; Shi, Xiaoran; Chen, Falai Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces. (English) Zbl 1388.13035 J. Comput. Appl. Math. 329, 2-23 (2018). Reviewer: Carlos Hermoso Ortíz (Madrid) MSC: 13D02 13P10 14Q05 14Q10 65D17 68U05 68U07 PDFBibTeX XMLCite \textit{X. Jia} et al., J. Comput. Appl. Math. 329, 2--23 (2018; Zbl 1388.13035) Full Text: DOI
Wang, Wei-Guo; Wei, Yimin Mixed and componentwise condition numbers for matrix decompositions. (English) Zbl 1375.65048 Theor. Comput. Sci. 681, 199-216 (2017). MSC: 65F05 15A23 65F35 PDFBibTeX XMLCite \textit{W.-G. Wang} and \textit{Y. Wei}, Theor. Comput. Sci. 681, 199--216 (2017; Zbl 1375.65048) Full Text: DOI
Bourne, Martin; Winkler, Joab R.; Yi, Su The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials. (English) Zbl 1353.65014 Appl. Numer. Math. 111, 17-35 (2017). MSC: 13P15 33C45 65F99 PDFBibTeX XMLCite \textit{M. Bourne} et al., Appl. Numer. Math. 111, 17--35 (2017; Zbl 1353.65014) Full Text: DOI Link
Schost, Éric; Spaenlehauer, Pierre-Jean A quadratically convergent algorithm for structured low-rank approximation. (English) Zbl 1347.65080 Found. Comput. Math. 16, No. 2, 457-492 (2016). Reviewer: Michael Jung (Dresden) MSC: 65F30 65Y20 15A83 65F10 PDFBibTeX XMLCite \textit{É. Schost} and \textit{P.-J. Spaenlehauer}, Found. Comput. Math. 16, No. 2, 457--492 (2016; Zbl 1347.65080) Full Text: DOI arXiv
Winkler, Joab R. Polynomial computations for blind image deconvolution. (English) Zbl 1357.68285 Linear Algebra Appl. 502, 77-103 (2016). MSC: 68U10 94A08 PDFBibTeX XMLCite \textit{J. R. Winkler}, Linear Algebra Appl. 502, 77--103 (2016; Zbl 1357.68285) Full Text: DOI
Winkler, Joab R. The Sylvester resultant matrix and image deblurring. (English) Zbl 1360.65078 Boissonnat, Jean-Daniel (ed.) et al., Curves and surfaces. 8th international conference, Paris, France, June 12–18, 2014. Revised selected papers. Cham: Springer (ISBN 978-3-319-22803-7/pbk; 978-3-319-22804-4/ebook). Lecture Notes in Computer Science 9213, 461-490 (2015). MSC: 65D18 PDFBibTeX XMLCite \textit{J. R. Winkler}, Lect. Notes Comput. Sci. 9213, 461--490 (2015; Zbl 1360.65078) Full Text: DOI Link
Shen, Li-Yong; Pérez-Díaz, Sonia Numerical proper reparametrization of parametric plane curves. (English) Zbl 1302.65049 J. Comput. Appl. Math. 277, 138-161 (2015). MSC: 65D17 PDFBibTeX XMLCite \textit{L.-Y. Shen} and \textit{S. Pérez-Díaz}, J. Comput. Appl. Math. 277, 138--161 (2015; Zbl 1302.65049) Full Text: DOI arXiv
Li, Zhe; Liu, Qi A heuristic verification of the degree of the approximate GCD of two univariate polynomials. (English) Zbl 1302.68333 Numer. Algorithms 67, No. 2, 319-334 (2014). MSC: 68W30 65H04 13P05 11A05 PDFBibTeX XMLCite \textit{Z. Li} and \textit{Q. Liu}, Numer. Algorithms 67, No. 2, 319--334 (2014; Zbl 1302.68333) Full Text: DOI
Christou, D.; Karcanias, N.; Mitrouli, M. Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials. (English) Zbl 1293.12007 J. Comput. Appl. Math. 260, 54-67 (2014). MSC: 12Y05 13P05 65H99 68W30 PDFBibTeX XMLCite \textit{D. Christou} et al., J. Comput. Appl. Math. 260, 54--67 (2014; Zbl 1293.12007) Full Text: DOI
Belhaj, Skander Computing the polynomial remainder sequence via Bézout matrices. (English) Zbl 1285.65022 J. Comput. Appl. Math. 250, 244-255 (2013). MSC: 65F30 PDFBibTeX XMLCite \textit{S. Belhaj}, J. Comput. Appl. Math. 250, 244--255 (2013; Zbl 1285.65022) 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
Batselier, Kim; Dreesen, Philippe; De Moor, Bart A geometrical approach to finding multivariate approximate LCMs and GCDs. (English) Zbl 1337.65033 Linear Algebra Appl. 438, No. 9, 3618-3628 (2013). MSC: 65F20 15A42 65F35 65F50 PDFBibTeX XMLCite \textit{K. Batselier} et al., Linear Algebra Appl. 438, No. 9, 3618--3628 (2013; Zbl 1337.65033) Full Text: DOI
Winkler, Joab R.; Lao, Xin; Hasan, Madina The computation of multiple roots of a polynomial. (English) Zbl 1243.65050 J. Comput. Appl. Math. 236, No. 14, 3478-3497 (2012). MSC: 65H04 12Y05 26C10 PDFBibTeX XMLCite \textit{J. R. Winkler} et al., J. Comput. Appl. Math. 236, No. 14, 3478--3497 (2012; Zbl 1243.65050) Full Text: DOI
Feng, Yong; Qin, Xiaolin; Zhang, Jingzhong; Yuan, Xun Obtaining exact interpolation multivariate polynomial by approximation. (English) Zbl 1259.65012 J. Syst. Sci. Complex. 24, No. 4, 803-815 (2011). MSC: 65D05 41A05 68W30 PDFBibTeX XMLCite \textit{Y. Feng} et al., J. Syst. Sci. Complex. 24, No. 4, 803--815 (2011; Zbl 1259.65012) Full Text: DOI arXiv
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
Winkler, Joab R.; Lao, Xin The calculation of the degree of an approximate greatest common divisor of two polynomials. (English) Zbl 1246.65062 J. Comput. Appl. Math. 235, No. 6, 1587-1603 (2011). MSC: 65F15 12Y05 26C05 PDFBibTeX XMLCite \textit{J. R. Winkler} and \textit{X. Lao}, J. Comput. Appl. Math. 235, No. 6, 1587--1603 (2011; Zbl 1246.65062) Full Text: DOI
Triantafyllou, Dimitrios; Mitrouli, Marilena On rank and null space computation of the generalized Sylvester matrix. (English) Zbl 1198.65082 Numer. Algorithms 54, No. 3, 297-324 (2010). Reviewer: Daniel Kressner (Berlin) MSC: 65F30 15B05 65F05 68W30 15A03 PDFBibTeX XMLCite \textit{D. Triantafyllou} and \textit{M. Mitrouli}, Numer. Algorithms 54, No. 3, 297--324 (2010; Zbl 1198.65082) Full Text: DOI
Terui, Akira GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials. (English) Zbl 1290.68139 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 12th international workshop, CASC 2010, Tsakhkadzor, Armenia, September 6–12, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15273-3/pbk). Lecture Notes in Computer Science 6244, 238-249 (2010). MSC: 68W30 12E05 12Y05 65D99 PDFBibTeX XMLCite \textit{A. Terui}, Lect. Notes Comput. Sci. 6244, 238--249 (2010; Zbl 1290.68139) Full Text: DOI arXiv
Winkler, Joab R.; Hasan, Madina A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix. (English) Zbl 1196.65083 J. Comput. Appl. Math. 234, No. 12, 3226-3242 (2010). MSC: 65F30 15A24 15A60 12E05 PDFBibTeX XMLCite \textit{J. R. Winkler} and \textit{M. Hasan}, J. Comput. Appl. Math. 234, No. 12, 3226--3242 (2010; Zbl 1196.65083) Full Text: DOI
Zeng, Zhonggang Regularization and matrix computation in numerical polynomial algebra. (English) Zbl 1191.65036 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 125-162 (2009). MSC: 65F15 68W30 13P15 13P10 PDFBibTeX XMLCite \textit{Z. Zeng}, in: Approximate commutative algebra. Berlin: Springer. 125--162 (2009; Zbl 1191.65036) Full Text: DOI
Winkler, Joab R.; Allan, John D. Structured total least norm and approximate GCDs of inexact polynomials. (English) Zbl 1136.65049 J. Comput. Appl. Math. 215, No. 1, 1-13 (2008). MSC: 65H05 11A05 11C08 PDFBibTeX XMLCite \textit{J. R. Winkler} and \textit{J. D. Allan}, J. Comput. Appl. Math. 215, No. 1, 1--13 (2008; Zbl 1136.65049) Full Text: DOI
Li, Bingyu; Liu, Zhuojun; Zhi, Lihong A structured rank-revealing method for Sylvester matrix. (English) Zbl 1140.65035 J. Comput. Appl. Math. 213, No. 1, 212-223 (2008). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 68W30 65Y20 15B57 15A03 PDFBibTeX XMLCite \textit{B. Li} et al., J. Comput. Appl. Math. 213, No. 1, 212--223 (2008; Zbl 1140.65035) Full Text: DOI
Zhang, Jingzhong; Feng, Yong Obtaining exact value by approximate computations. (English) Zbl 1202.68494 Sci. China, Ser. A 50, No. 9, 1361-1368 (2007). MSC: 68W30 11A55 11J70 33F10 65D99 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{Y. Feng}, Sci. China, Ser. A 50, No. 9, 1361--1368 (2007; Zbl 1202.68494) Full Text: DOI arXiv