Algorithm 748 swMATH ID: 13186 Software Authors: Alefeld, G.E.; Potra, F.A.; Shi, Yixun Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=210111 Keywords: root enclosing algorithm; inverse cubic interpolation; algorithms; Brent’s method Related Software: RROOT_748; BRENT; RRK_rr; MINLP; Bonmin; Boost; Ipopt; SHOT; PAVER; ANTIGONE; OSiL; AlphaECP; DICOPT; Boost C++ Libraries; BARON; NeuralPDE.jl; DifferentialEquations.jl; GitHub; Julia; Matplotlib Cited in: 15 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 748; enclosing zeros of continuous functions. Zbl 0872.65041Alefeld, G. E.; Potra, F. A.; Shi, Yixun 1995 all top 5 Cited by 26 Authors 3 Alefeld, Götz E. 3 Potra, Florian-Alexandru 3 Ranocha, Hendrik 2 Dalcín, Lisandro D. 2 Ketcheson, David I. 2 Kronqvist, Jan 2 Lundell, Andreas 2 Parsani, Matteo 2 Shi, Yixun 2 Westerlund, Tapio 1 Abaffy, Jozsef 1 Bohn, Tanner A. 1 Costabile, Francesco Aldo 1 De Luna, Manuel Quezada 1 Galántai, Aurél 1 Green, Kevin R. 1 Gualtieri, Maria Italia 1 Jahdali, Rasha Al 1 Le Floc’h, Fabien 1 Luceri, Rossana 1 Mitsotakis, Dimitrios E. 1 Oosterlee, Cornelis Willebrordus 1 Romm, Ya. E. 1 Spiteri, Raymond J. 1 Völker, Wolfgang 1 Yaroshenko, I. all top 5 Cited in 13 Serials 2 ACM Transactions on Mathematical Software 2 Journal of Global Optimization 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 BIT 1 Calcolo 1 Numerical Algorithms 1 Cybernetics and Systems Analysis 1 SIAM Journal on Scientific Computing 1 Journal of Mathematical Sciences (New York) 1 Decisions in Economics and Finance 1 Communications in Computational Physics 1 SN Partial Differential Equations and Applications all top 5 Cited in 8 Fields 11 Numerical analysis (65-XX) 2 Partial differential equations (35-XX) 2 Computer science (68-XX) 2 Fluid mechanics (76-XX) 2 Operations research, mathematical programming (90-XX) 1 Ordinary differential equations (34-XX) 1 Statistics (62-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year