Algorithm 748: Enclosing zeros of continuous functions Two efficient algorithms for enclosing a zero of a continuous function are presented. They are similar to the recent methods, but together with quadratic interpolation they make essential use of inverse cubic interpolation as well. Since asymptotically the inverse cubic interpolation is always chosen by the algorithms, they achieve higher-efficiency indices: 1.6529… for the first algorithm, and 1.6686… for the second one. It is proved that the second algorithm is optimal in a certain family. Numerical experiments show that the two new methods compare well with recent methods, as well as with the efficient solvers of Dekker, Brent, Bus and Dekker, and Le. The second method from the present article has the best behavior of all 12 methods especially when the termination tolerance is small. (Source: http://dl.acm.org/)

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References in zbMATH (referenced in 12 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. Alefeld, G. E.; Potra, F. A.; Völker, W.: Modifications of the interval-Newton-method with improved asymptotic efficiency (1998)
  11. Alefeld, G. E.; Potra, F. A.; Shi, Y.: Algorithm 748: Enclosing zeros of continuous functions (1995)
  12. Alefeld, G. E.; Potra, F. A.; Shi, Yixun: Algorithm 748; enclosing zeros of continuous functions (1995)