Bertini

Bertini™: Software for Numerical Algebraic Geometry. Software for solving polynomial systems. Finds isolated solutions using total-degree start systems, multihomogeneous-degree start systems, and also user defined homotopies. Implements parameter continuation for families of systems, such as the inverse kinematics of six-revolute serial-link arms, or the forward kinematics of Stewart-Gough parallel-link robots. Adaptive multiprecision implemented for finding isolated solutions and for the numerical irreducible decomposition. Treats positive-dimensional solutions by computing witness sets. Has automatic differentiation which preserves the straightline quality of an input system. Uses homogenization to accurately compute solutions ”at infinity.” Provides a fractional power-series endgame to accurately compute singular roots Allows for subfunctions. Allows for witness set manipulation via both sampling and membership testing. Accepts square or nonsquare systems.


References in zbMATH (referenced in 147 articles , 1 standard article )

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  1. Angelini, Elena; Bocci, Cristiano; Chiantini, Luca: Real identifiability vs. complex identifiability (2018)
  2. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  3. Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes: Certifying solutions to overdetermined and singular polynomial systems over $\mathbbQ$ (2018)
  4. Bernardi, Alessandra; Gimigliano, Alessandro; Idà, Monica: Singularities of plane rational curves via projections (2018)
  5. Boeck, Thomas; Terzijska, Džulia; Eichfelder, Gabriele: Maximum electromagnetic drag configurations for a translating conducting cylinder with distant magnetic dipoles (2018)
  6. Coss, Owen; Hauenstein, Jonathan D.; Hong, Hoon; Molzahn, Daniel K.: Locating and counting equilibria of the Kuramoto model with rank-one coupling (2018)
  7. Hao, Wenrui: A homotopy method for parameter estimation of nonlinear differential equations with multiple optima (2018)
  8. Helmer, Martin; Sturmfels, Bernd: Nearest points on toric varieties (2018)
  9. Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping: Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity (2018)
  10. Steger, Carsten: Algorithms for the orthographic-$n$-point problem (2018)
  11. Baharev, Ali; Domes, Ferenc; Neumaier, Arnold: A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations (2017)
  12. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  13. Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard: Tensor decomposition and homotopy continuation (2017)
  14. Boralevi, Ada; van Doornmalen, Jasper; Draisma, Jan; Hochstenbach, Michiel E.; Plestenjak, Bor: Uniform determinantal representations (2017)
  15. Breiding, Paul: The expected number of eigenvalues of a real Gaussian tensor (2017)
  16. Brown, David A.; Zingg, David W.: Design and evaluation of homotopies for efficient and robust continuation (2017)
  17. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  18. Cifuentes, Diego; Parrilo, Pablo A.: Sampling algebraic varieties for sum of squares programs (2017)
  19. Compagnoni, Marco; Notari, Roberto; Antonacci, Fabio; Sarti, Augusto: On the statistical model of source localization based on range difference measurements (2017)
  20. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)

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