Numerical Analysis: UNIT 1 - Part 1
Numerical Analysis: UNIT 1 - Part 1
Numerical Analysis: UNIT 1 - Part 1
2019
UNIT 1 – part 1
Root Finding Problems
Zeros of a Function
Simple Zeros
Facts
o Any nth order polynomial has exactly n zeros (counting real and
o Any polynomial with an odd order has at least one real zero.
the function and its first (m-1) derivatives are zero at x=r
Analytical Methods
Bracketing Methods
■ Bisection method
Open Methods
In the open methods, the method starts with one or more initial
Example 1
Bisection Method
Bisection Algorithm
Disadvantage
o Slow to converge
Example 1
Stopping Criteria
o Convergence Analysis
Example 1
F(x)=x-cos(x)
Newton’s Method
o If the initial guess of the root is far from the root the method
f’(r) =0}.
o Flat Spot
o Cycle
Example 1