Algorithm 748

Algorithm 748; enclosing zeros of continuous functions. The authors present two new modifications of their previously published algorithms for enclosing a zero of a continuous function $f(x)$. The modifications involve the use of inverse cubic interpolation rather than quadratic interpolation. The paper also discusses their earlier algorithms, and compares these algorithms with other standard routines. Although the new algorithms are marginally more economical in terms of function evaluations, it is striking how well Brent’s method compares in practice, 25 years after its introduction.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Ranocha, Hendrik; de Luna, Manuel Quezada; Ketcheson, David I.: On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations (2021)
  2. Ranocha, Hendrik; Mitsotakis, Dimitrios; Ketcheson, David I.: A broad class of conservative numerical methods for dispersive wave equations (2021)
  3. Ranocha, Hendrik; Dalcin, Lisandro; Parsani, Matteo: Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier-Stokes equations (2020)
  4. Green, Kevin R.; Bohn, Tanner A.; Spiteri, Raymond J.: Direct function evaluation versus lookup tables: when to use which? (2019)
  5. Le Floc’h, Fabien; Oosterlee, Cornelis W.: Model-free stochastic collocation for an arbitrage-free implied volatility. I. (2019)
  6. Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio: The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming (2016)
  7. Yaroshenko, I.: On robust algorithm for finding maximum likelihood estimation of the generalized inverse Gaussian distribution (2016)
  8. Galántai, Aurel; Abaffy, Jozsef: Always convergent iteration methods for nonlinear equations of Lipschitz functions (2015)
  9. Costabile, F.; Gualtieri, M. I.; Luceri, R.: A modification of Muller’s method (2006)
  10. Romm, Ya. E.: Sorting-based calculation of zeros and extrema of functions as applied to search and recognition. II (2001)
  11. Alefeld, G. E.; Potra, F. A.; Völker, W.: Modifications of the interval-Newton-method with improved asymptotic efficiency (1998)
  12. Alefeld, G. E.; Potra, F. A.; Shi, Y.: Algorithm 748: Enclosing zeros of continuous functions (1995)
  13. Alefeld, G. E.; Potra, F. A.; Shi, Yixun: Algorithm 748; enclosing zeros of continuous functions (1995)