ABSTRACT
Numerical methods for solving an equation are divided into three main categories namely: bracketing methods, open methods, and using the built-in MATLAB function fzero. The fzero function uses a combination of the bisection, secant, and inverse quadratic interpolation methods. The regula falsi method can be modified such that both ends of the interval move toward the root, thus improving the rate of convergence. Two types of convergence can be exhibited by the fixed-point iteration namely: monotone and oscillatory. In a monotone convergence, the elements of the generated sequence converge to the fixed point from one side, while in an oscillatory convergence, the elements bounce from one side of the fixed point to the other as they approach it. For the case of a simple root, the rate of convergence for the secant method is 1.618, thus the generated sequence converges faster than the linear but slower than the quadratic.
