Advantages and Disadvanteges of Secant Method

Advantages of secant method:

1. It converges at faster than a linear rate, so that it is more rapidly
convergent than the bisection method.
2. It does not require use of the derivative of the
function, something that is not available in a number
of applications.
3. It requires only one function evaluation per iteration,
as compared with Newton’s method which requires
two.
Disadvantages of secant method:
1. It may not converge.
2. There is no guaranteed error bound for the computed
iterates.
3. It is likely to have difficulty if f 0(α) = 0. This
means the x-axis is tangent to the graph of y = f (x)
at x = α.
4. Newton’s method generalizes more easily to new
methods for solving simultaneous systems of nonlinear
equations.