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alphaCertified

swMATH ID: 7351
Software Authors: Jonathan D. Hauenstein; Frank Sottile
Description: Algorithm 921: alphaCertified: Certifying solutions to polynomial systems. Smale’s α-theory uses estimates related to the convergence of Newton’s method to certify that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements algorithms based on α-theory to certify solutions of polynomial systems using both exact rational arithmetic and arbitrary precision floating point arithmetic. It also implements algorithms that certify whether a given point corresponds to a real solution, and algorithms to heuristically validate solutions to overdetermined systems. Examples are presented to demonstrate the algorithms.
Homepage: http://dl.acm.org/citation.cfm?id=2331136
Related Software: Bertini; Macaulay2; PHCpack; HOM4PS; NumericalAlgebraicGeometry; SINGULAR; ISOLATE; NAG4M2; Magma; MonodromySolver; HomotopyContinuation; INTLAB; PHoM; MixedVol; Paramotopy; NewtonLib; MultRoot; STRINGVACUA; CoCoA; Algorithm 931
Cited in: 56 Publications
all top 5

Cited by 88 Authors

22 Hauenstein, Jonathan D.
11 Sottile, Frank
7 Szántó, Ágnes
5 Mehta, Dhagash
4 Hein, Nickolas
4 Timme, Sascha
3 Bates, Daniel J.
3 Cheng, Jinsan
3 Dou, Xiaojie
3 Leykin, Anton
3 Niemerg, Matthew E.
3 Sommese, Andrew John
2 Breiding, Paul
2 Brysiewicz, Taylor
2 del Campo, Abraham Martín
2 Duff, Timothy
2 Harris, Katherine M.
2 He, Yang-Hui Evariste
2 Lee, Kisun
2 Lee, Tsung-Lin
2 Regan, Margaret H.
1 Alaeddini, Adel
1 Ayyildiz Akoglu, Tulay
1 Beltrán, Carlos
1 Bernal, Edgar A.
1 Bozóki, Sándor
1 Brake, Daniel A.
1 Brake, Danielle A.
1 Brustenga i Moncusí, Laura
1 Burr, Michael A.
1 Chen, Tianran
1 Decker, Wolfram
1 Do, Ngoc T.
1 Frohmader, Andrew
1 García Puente, Luis David
1 Griffin, Zachary A.
1 Gross, Elizabeth
1 Heaton, Alexander
1 Helmer, Martin
1 Hill, Cvetelina
1 Hillar, Christopher J.
1 Imbach, Rémi
1 Jensen, Anders Nedergaard
1 Kaluba, Marek
1 Kuchment, Peter A.
1 Kulkarni, Avinash
1 Lairez, Pierre
1 Levandovskyy, Viktor
1 Li, Tien-Yien
1 Li, Zhe
1 Liddell, Alan C. jun.
1 Lorenz, Benjamin
1 Manivel, Laurent
1 Mantzaflaris, Angelos
1 Moroz, Guillaume
1 Mourrain, Bernard
1 Oeding, Luke
1 Ottaviani, Giorgio Maria
1 Pan, Victor Yakovlevich
1 Peterson, Chris
1 Pfister, Gerhard
1 Pouget, Marc
1 Rodriguez, Jose Israel
1 Rónyai, Lajos
1 Ruatta, Olivier
1 Ruffo, James
1 Schreyer, Frank-Olaf
1 Sciabica, Mark
1 Sertöz, Emre Can
1 Shen, Fei
1 Sherman, Samantha N.
1 Shirinkam, Sara
1 Sommars, Jeff
1 Sturmfels, Bernd
1 Sun, Chuang
1 Szendrői, Balázs
1 Tang, Tingting
1 Teitler, Zach
1 Vinzant, Cynthia
1 Wampler, Charles W. II
1 Wan, Baocheng
1 Weinstein, Madeleine
1 Wen, Junyi
1 Wu, Wenyuan
1 Xia, Bican
1 Yahl, Thomas
1 Zhang, Shugong
1 Zhi, Lihong

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