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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; Boost; Boost C++ Libraries; GitHub; FFTW; PETSc; zeroin; SHOT; PAVER; ANTIGONE; OSiL; AlphaECP; DICOPT; Ipopt; MINLP; Bonmin; BARON; Julia
Cited in:	18 Documents

1 Publication describing the Software, including 1 Publication in zbMATH	Year
Algorithm 748; enclosing zeros of continuous functions. Zbl 0872.65041 Alefeld, G. E.; Potra, F. A.; Shi, Yixun	1995

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3	Alefeld, Götz E.
3	Potra, Florian-Alexandru
3	Ranocha, Hendrik
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2	Fernández-Díaz, Julio M.
2	Ketcheson, David I.
2	Kronqvist, Jan
2	Lundell, Andreas
2	Menéndez Pérez, César O.
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
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1	Green, Kevin R.
1	Gualtieri, Maria Italia
1	Jahdali, Rasha Al
1	Le Floc’h, Fabien
1	Luceri, Rossana
1	Mitsotakis, Dimitrios E.
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1	Romm, Ya. E.
1	Sahlin, Ullrika
1	Spiteri, Raymond J.
1	Völker, Wolfgang
1	Yaroshenko, I.

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