Giusti, Marc; Yakoubsohn, Jean-Claude Numerical approximation of multiple isolated roots of analytical systems. (Approximation numérique de racines isolées multiples de systèmes analytiques.) (French. English summary) Zbl 1453.65107 Ann. Henri Lebesgue 3, 901-957 (2020). MSC: 65H10 65Y20 68Q25 68W30 PDF BibTeX XML Cite \textit{M. Giusti} and \textit{J.-C. Yakoubsohn}, Ann. Henri Lebesgue 3, 901--957 (2020; Zbl 1453.65107) Full Text: DOI
Burr, Michael; Gao, Shuhong; Tsigaridas, Elias The complexity of subdivision for diameter-distance tests. (English) Zbl 1444.68274 J. Symb. Comput. 101, 1-27 (2020). MSC: 68U05 14Q20 68W30 68W40 PDF BibTeX XML Cite \textit{M. Burr} et al., J. Symb. Comput. 101, 1--27 (2020; Zbl 1444.68274) Full Text: DOI
Cheng, Jin-San; Dou, Xiaojie; Wen, Junyi A new deflation method for verifying the isolated singular zeros of polynomial systems. (English) Zbl 1434.65074 J. Comput. Appl. Math. 376, Article ID 112825, 21 p. (2020). MSC: 65H10 PDF BibTeX XML Cite \textit{J.-S. Cheng} et al., J. Comput. Appl. Math. 376, Article ID 112825, 21 p. (2020; Zbl 1434.65074) Full Text: DOI
Hao, Zhiwei; Jiang, Wenrong; Li, Nan; Zhi, Lihong On isolation of simple multiple zeros and clusters of zeros of polynomial systems. (English) Zbl 07146720 Math. Comput. 89, No. 322, 879-909 (2020). MSC: 65H10 74G35 68W30 32-04 32S99 PDF BibTeX XML Cite \textit{Z. Hao} et al., Math. Comput. 89, No. 322, 879--909 (2020; Zbl 07146720) Full Text: DOI
Kim, Myong-Hi; Martens, Marco; Sutherland, Scott Geometry of polynomials and root-finding via path-lifting. (English) Zbl 1386.65139 Nonlinearity 31, No. 2, 414-457 (2018). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 65H05 65H10 30C15 37F10 68Q25 PDF BibTeX XML Cite \textit{M.-H. Kim} et al., Nonlinearity 31, No. 2, 414--457 (2018; Zbl 1386.65139) Full Text: DOI
Becker, Ruben; Sagraloff, Michael; Sharma, Vikram; Yap, Chee A near-optimal subdivision algorithm for complex root isolation based on the Pellet test and Newton iteration. (English) Zbl 1383.65043 J. Symb. Comput. 86, 51-96 (2018). MSC: 65H04 65E05 30C15 65Y20 PDF BibTeX XML Cite \textit{R. Becker} et al., J. Symb. Comput. 86, 51--96 (2018; Zbl 1383.65043) Full Text: DOI arXiv
Strzeboński, Adam; Tsigaridas, Elias P. Univariate real root isolation over a single logarithmic extension of real algebraic numbers. (English) Zbl 1393.11086 Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 425-445 (2017). MSC: 11Y16 11R04 12D10 68W30 PDF BibTeX XML Cite \textit{A. Strzeboński} and \textit{E. P. Tsigaridas}, in: Applications of computer algebra, Kalamata, Greece, July 20--23, 2015. Cham: Springer. 425--445 (2017; Zbl 1393.11086) Full Text: DOI
Schleicher, Dierk; Stoll, Robin Newton’s method in practice: finding all roots of polynomials of degree one million efficiently. (English) Zbl 1375.65068 Theor. Comput. Sci. 681, 146-166 (2017). MSC: 65H04 65E05 30C15 PDF BibTeX XML Cite \textit{D. Schleicher} and \textit{R. Stoll}, Theor. Comput. Sci. 681, 146--166 (2017; Zbl 1375.65068) Full Text: DOI
Batra, Prashant; Sharma, Vikram Near optimal subdivision algorithms for real root isolation. (English) Zbl 1375.65064 J. Symb. Comput. 83, 4-35 (2017). MSC: 65H04 65G30 PDF BibTeX XML Cite \textit{P. Batra} and \textit{V. Sharma}, J. Symb. Comput. 83, 4--35 (2017; Zbl 1375.65064) Full Text: DOI
Scott, T. C.; Zhang, Wenxing Efficient hybrid-symbolic methods for quantum mechanical calculations. (English) Zbl 1344.81028 Comput. Phys. Commun. 191, 221-234 (2015). MSC: 81-04 81V55 PDF BibTeX XML Cite \textit{T. C. Scott} and \textit{W. Zhang}, Comput. Phys. Commun. 191, 221--234 (2015; Zbl 1344.81028) Full Text: DOI
Li, Zhe; Sang, Haifeng Verified error bounds for singular solutions of nonlinear systems. (English) Zbl 1328.65121 Numer. Algorithms 70, No. 2, 309-331 (2015). Reviewer: Anton Iliev (Plovdiv) MSC: 65H10 13P05 11A05 PDF BibTeX XML Cite \textit{Z. Li} and \textit{H. Sang}, Numer. Algorithms 70, No. 2, 309--331 (2015; Zbl 1328.65121) Full Text: DOI
Mehlhorn, Kurt; Sagraloff, Michael; Wang, Pengming From approximate factorization to root isolation with application to cylindrical algebraic decomposition. (English) Zbl 1357.68305 J. Symb. Comput. 66, 34-69 (2015). MSC: 68W30 14Q05 30C15 65H04 68W40 PDF BibTeX XML Cite \textit{K. Mehlhorn} et al., J. Symb. Comput. 66, 34--69 (2015; Zbl 1357.68305) Full Text: DOI
Li, Nan; Zhi, Lihong Verified error bounds for isolated singular solutions of polynomial systems: case of breadth one. (English) Zbl 1291.65161 Theor. Comput. Sci. 479, 163-173 (2013). MSC: 65H10 68W30 13P15 65G20 PDF BibTeX XML Cite \textit{N. Li} and \textit{L. Zhi}, Theor. Comput. Sci. 479, 163--173 (2013; Zbl 1291.65161) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{G. Chèze} et al., Theor. Comput. Sci. 412, No. 35, 4493--4503 (2011; Zbl 1221.68297) Full Text: DOI
Haller-Dintelmann, R.; Kaiser, H.-Ch.; Rehberg, J. Direct computation of elliptic singularities across anisotropic, multi-material edges. (English. Russian original) Zbl 1222.35075 J. Math. Sci., New York 172, No. 4, 589-622 (2011); translation from Probl. Mat. Anal. 53, 141-170 (2010). MSC: 35J25 35J75 PDF BibTeX XML Cite \textit{R. Haller-Dintelmann} et al., J. Math. Sci., New York 172, No. 4, 589--622 (2011; Zbl 1222.35075); translation from Probl. Mat. Anal. 53, 141--170 (2010) Full Text: DOI
Batra, Prashant Globally convergent, iterative path-following for algebraic equations. (English) Zbl 1229.65076 Math. Comput. Sci. 4, No. 4, 507-537 (2010). MSC: 65H04 26C10 68W30 PDF BibTeX XML Cite \textit{P. Batra}, Math. Comput. Sci. 4, No. 4, 507--537 (2010; Zbl 1229.65076) Full Text: DOI
Durvye, Clémence Evaluation techniques for zero-dimensional primary decomposition. (English) Zbl 1221.13043 J. Symb. Comput. 44, No. 9, 1089-1113 (2009). MSC: 13P15 68W30 12Y05 PDF BibTeX XML Cite \textit{C. Durvye}, J. Symb. Comput. 44, No. 9, 1089--1113 (2009; Zbl 1221.13043) Full Text: DOI
Pope, Scott R.; Szanto, Agnes Nearest multivariate system with given root multiplicities. (English) Zbl 1168.65347 J. Symb. Comput. 44, No. 6, 606-625 (2009). MSC: 65H10 13P15 68W30 PDF BibTeX XML Cite \textit{S. R. Pope} and \textit{A. Szanto}, J. Symb. Comput. 44, No. 6, 606--625 (2009; Zbl 1168.65347) Full Text: DOI
Proinov, Petko D. General local convergence theory for a class of iterative processes and its applications to Newton’s method. (English) Zbl 1158.65040 J. Complexity 25, No. 1, 38-62 (2009). Reviewer: Erwin Schechter (Moers) MSC: 65J15 47J25 65H05 65E05 30C15 PDF BibTeX XML Cite \textit{P. D. Proinov}, J. Complexity 25, No. 1, 38--62 (2009; Zbl 1158.65040) Full Text: DOI
Beltrán, Carlos; Pardo, Luis Miguel On the probability distribution of singular varieties of given corank. (English) Zbl 1149.11038 J. Symb. Comput. 42, No. 1-2, 4-29 (2007). MSC: 11K36 PDF BibTeX XML Cite \textit{C. Beltrán} and \textit{L. M. Pardo}, J. Symb. Comput. 42, No. 1--2, 4--29 (2007; Zbl 1149.11038) Full Text: DOI
Leykin, Anton; Verschelde, Jan; Zhao, Ailing Newton’s method with deflation for isolated singularities of polynomial systems. (English) Zbl 1106.65046 Theor. Comput. Sci. 359, No. 1-3, 111-122 (2006). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 65H10 68W30 12Y05 26C10 30C15 65H20 PDF BibTeX XML Cite \textit{A. Leykin} et al., Theor. Comput. Sci. 359, No. 1--3, 111--122 (2006; Zbl 1106.65046) Full Text: DOI arXiv
Yakoubsohn, J.-C. Numerical analysis of a bisection-exclusion method to find zeros of univariate analytic functions. (English) Zbl 1084.65055 J. Complexity 21, No. 5, 652-690 (2005). Reviewer: Vasile Berinde (Baia Mare) MSC: 65H05 65E05 30C15 PDF BibTeX XML Cite \textit{J. C. Yakoubsohn}, J. Complexity 21, No. 5, 652--690 (2005; Zbl 1084.65055) Full Text: DOI