Muller's Method
Background
Muller's
method is a generalization of the secant
method, in the sense that it does not require the derivative of the function. It
is an iterative method that requires three starting points,
,
and
.A
parabola is constructed that passes through the three points; then the quadratic
formula is used to find a root of the quadratic for the next approximation.It
has been proved that near a simple root Muller's method converges faster than
the secant method and almost as fast as Newton's method.The method can be used
to find real or complex zeros of a function and can be programmed to use complex
arithmetic.
Mathematica Subroutine (Newton-Raphson Iteration).
Mathematica Subroutine (Muller's Method).
Example.Use Newton's method and
Muller's method to find numerical approximations to the multiple rootof
the function.
Show details of the computations for the starting value.Compare
the number of iterations for the two methods.
Solution.
|