Muller Method

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Iteration scheme is simple to implement.
Iterations always converge for any continuous function f(x).

Disadvantages

Convergence process is slow.
Always one has to find the interval [a,b] which brackets the zero of f(x)= 0 more importantly f(a) * f(b) must be less than zero.

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1. Find the root of (cos[x])-(x * exp[x]) = 0 exp1.jpg for (cos[x])-(x * exp[x])

The graph of this equation is given in the figure.

Let the initial guess be 1.0 and 2.0

i	0	1	2	3	4	5	6	7	8
x_i	1	2	0.83267	0.72878	0.56240	0.52478	0.51801	0.51776	0.51776

So the iterative process converges at 0.51776

2. Find the root of x⁴-x-10 = 0 exp2.jpg for x^4-x-10