A Root-finding Algorithm which combines root bracketing, bisection, and Inverse Quadratic Interpolation. It is sometimes known as the van Wijngaarden-Deker-Brent Method.

Brent's method uses a Lagrange Interpolating Polynomial of degree 2. Brent (1973) claims that this method will always converge as long as the values of the function are computable within a given region containing a Root. Given three points , , and , Brent's method fits as a quadratic function of , then uses the interpolation formula

(1) |

(2) |

(3) | |||

(4) |

with

(5) | |||

(6) | |||

(7) |

(Press

**References**

Brent, R. P. Ch. 3-4 in *Algorithms for Minimization Without Derivatives.* Englewood Cliffs, NJ: Prentice-Hall, 1973.

Forsythe, G. E.; Malcolm, M. A.; and Moler, C. B. §7.2 in *Computer Methods for Mathematical Computations.*
Englewood Cliffs, NJ: Prentice-Hall, 1977.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Van Wijngaarden-Dekker-Brent Method.''
§9.3 in *Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England: Cambridge
University Press, pp. 352-355, 1992.

© 1996-9

1999-05-26