In numerical analysis, Brent's method is a complicated but popular 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.
在数值分析领域，Brent方法是一个复杂的、但是却很流行的寻根算法，它结合了二分法、割线法以及反向二次插值法的特点。它具有二分法的稳定性，但是它的速度却可与一些不太稳定的方法相比拟。

Detail on Brent's method：

http://en.wikipedia.org/wiki/Brent%27s_method

Why mention Brent's method：

Powell's method, strictly Powell's conjugate gradient descent method（Powell的共轭梯度下降法）, is an algorithm for finding the local minimum of a function. The function need not be differentiable（可微）, and no derivatives（导数） are taken.

The function must be a real-valued function of a fixed number of real-valued inputs, creating an N-dimensional hypersurface or Hamiltonian.^{[disambiguation needed]} The caller passes in the initial point. The callers also passes in a set of initial search vectors. Typically N search vectors are passed in which are simply the normals aligned to each axis.

The method minimises the function by a bi-directional search along each search vector, in turn. The new position can then be expressed as a linear combination of the search vectors. The new displacement vector becomes a new search vector, and is added to the end of the search vector list. Meanwhile the search vector which contributed most to the new direction, i.e. the one which was most successful, is deleted from the search vector list. The algorithm iterates an arbitrary number of times until no significant improvement is made.

The method is useful for calculating the local minimum of a continuous but complex function, especially one without an underlying mathematical definition, because it is not necessary to take derivatives. The basic algorithm is simple, the complexity is in the linear searches along the search vectors, which can be achieved via Brent's method.

Extended reading：

http://math.fullerton.edu/mathews/n2003/BrentMethodMod.html

http://mathworld.wolfram.com/BrentsMethod.html

http://reference.wolfram.com/mathematica/tutorial/UnconstrainedOptimizationBrentsMethod.html

Detail on Powell's method：

http://en.wikipedia.org/wiki/Powell's_method

Something more related with Powell's method：

http://www.efunda.com/math/leastsquares/leastsquares.cfm#PageTop

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