Muller's method is an extension of the secant method used to approximate complex roots of real equations. It relies on real starting approximations and involves a specific theorem regarding roots with multiplicities. The document also includes derivation, an iteration process, graphical representation, and a Python code example related to Muller's method.

1. MULLER METHOD
Name: Shrinivas Shiddharoodha Hongal
Roll no.: 231ME151
Department: Mechanical Engineering
Section: M1
Numerical Methods -
MA207

2. • The Muller's Method is an extension of the Secant
Method.
• It is conveniently used to approximate a complex root
of a real equation, using real starting approximations
or just a real root.
• THEOREM: If z = a + bi is a complex zero of multiplicity
m of the polynomial p(x) with real coefficients, then
overline z = a - bi is also a zero of multiplicity m of the
polynomial p(x), and is a
factor of p(x)
Whats is Muller’s
Method?

3. Derivation

4. -4

5. Iteration
Process

7. Graph
Using Secant method Using Muller method

8. Algorithm

10. Python Code

11. Example
Sample
Problem

12. Thank
You