Computing common zeros of two bivariate function: r = rootsb(f,g,xydomain) finds the common zeros of two bivariate functions f and g in the domain xydomain (4-element vector), which are given as function handles. This code exists besides roots(f,g) in chebfun2 (which does essentially the same task) because it is sometimes better for accuracy to resample the functions when working in a subdivided, smaller domain. If xydomain is not provided, it defaults to [-1 1 -1 1]. test.m runs a simple test and shows the plots of the solution along with the zero curves. The solutions should be the intersections of the curves. This code always employs the algorithm based on the hidden variable resultant method. For the algorithmic details, see 1] Y. Nakatsukasa, V. Noferini, and A. Townsend, Computing the common zeros of two bivariate functions via Bezout resultants, submitted (2013).

References in zbMATH (referenced in 14 articles )

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  1. Mourrain, Bernard; Telen, Simon; Van Barel, Marc: Truncated normal forms for solving polynomial systems: generalized and efficient algorithms (2021)
  2. Telen, Simon: Numerical root finding via Cox rings (2020)
  3. Nakatsukasa, Yuji; Noferini, Vanni: Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems (2019)
  4. Kaushansky, Vadim; Lipton, Alexander; Reisinger, Christoph: Transition probability of Brownian motion in the octant and its application to default modelling (2018)
  5. Boralevi, Ada; van Doornmalen, Jasper; Draisma, Jan; Hochstenbach, Michiel E.; Plestenjak, Bor: Uniform determinantal representations (2017)
  6. Nakatsukasa, Yuji; Noferini, Vanni; Townsend, Alex: Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach (2017)
  7. Nakatsukasa, Yuji; Noferini, Vanni: On the stability of computing polynomial roots via confederate linearizations (2016)
  8. Noferini, Vanni; Townsend, Alex: Numerical instability of resultant methods for multidimensional rootfinding (2016)
  9. Plestenjak, Bor; Hochstenbach, Michiel E.: Roots of bivariate polynomial systems via determinantal representations (2016)
  10. Sakaue, Shinsaku; Nakatsukasa, Yuji; Takeda, Akiko; Iwata, Satoru: Solving generalized CDT problems via two-parameter eigenvalues (2016)
  11. Aruliah, D. A.; Corless, R. M.; Diaz-Toca, G. M.; Gonzalez-Vega, L.; Shakoori, A.: The Bézout matrix for Hermite interpolants (2015)
  12. Hochstenbach, Michiel E.; Muhič, Andrej; Plestenjak, Bor: Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems (2015)
  13. Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Computing the signed distance between overlapping ellipsoids (2015)
  14. Nakatsukasa, Yuji; Noferini, Vanni; Townsend, Alex: Computing the common zeros of two bivariate functions via Bézout resultants (2015)