NonLinearBrent.hpp File Reference

Implementation of Brent's method for root finding. More...

#include <limits>
#include <lifev/core/LifeV.hpp>

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Namespaces
	LifeV
	Default Physical Solver.

Functions
template<class Function >
Real	NonLinearBrent (const Function &f, const Real &leftExtremeBase, const Real &rightExtremeBase, const Real &toll, const UInt &maxIter)
	Implementation of Brent's method for root finding. More...

Detailed Description

Implementation of Brent's method for root finding.

Author

Alessio Fumagalli aless.nosp@m.io.f.nosp@m.umaga.nosp@m.lli@.nosp@m.mail..nosp@m.poli.nosp@m.mi.it

Date

Contributor:

Alessandro Melani aless.nosp@m.andr.nosp@m.o.mel.nosp@m.ani@.nosp@m.mail..nosp@m.poli.nosp@m.mi.it Alessandro Melani aless.nosp@m.andr.nosp@m.o.mel.nosp@m.ani@.nosp@m.mail..nosp@m.poli.nosp@m.mi.it

Brent's method is a root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less reliable methods. The idea is to use the secant method or inverse quadratic interpolation if possible, because they converge faster, but to fall back to the more robust bisection method if necessary.

See also

Chapter 4 of R.P. Brent, "Algorithms for Minimization without Derivatives", Prentice-Hall, Englewood Cliffs, NJ. 1973

Definition in file NonLinearBrent.hpp.