Why use Quasi-Newton method over Newton Raphson?
I’m mostly quoting from Numerical Recipes in C. “In this section, we will discuss the simplest multidimensional root finding method, Newton-Raphson. The method gives you a very efficient means of converging to a root, if you have a sufficiently good initial guess. It can also spectactularly fail to converge, indicating (though not proving) that your putative root does not exist nearby. In 9.7 we discuss more sophisticated implementations of the Newton-Raphson method, which try to improve on Newton-Raphson’s poor global convergence. A multidimensional generalization of the secant method, called Broyden’s method is also discussed in 9.7” Broyden’s method is supposed to be Quasi-Newton. Supposedly one advantage of the Quasi-Newton methods over Newton Raphson is that they don’t require the Jacobian matrix which is very expensive.
