The document outlines various numerical methods for solving complex problems through algorithms and simple operations, including the Muller, Chebyshev, fixed point iteration, Aitken's delta square, Birge Vieta, and Bairstow methods. It discusses their advantages such as effective problem-solving capabilities in scenarios where analytical methods fail, while noting their limitations in providing approximate solutions. Applications of these methods span across weather predictions, vehicle simulations, spacecraft navigation, and financial calculations.

1. NUMERICAL METHODS
Presented By : Amogha.A.K.
EEE- DEPARTMENT

2. Contents
• Introduction
• Muller Method
• Chebyshev Method
• Fixed Point Iteration Method
• Aitken’s Delta Square Method
• Birge Vieta Method
• Bairstow Method
• Advantages Of Numerical Methods
• Disadvantage Of Numerical Methods
• Applications
• Conclusions
• References

3. Introduction
 It is the study of algorithms that use
numerical approximations.
This gives solutions for complex problems.
This uses simple mathematical operations.

4. Muller Method
•It obtains a root
estimate by projecting
a parabola to the x-axis
through three function
values.

5. FORMULAE FOR MULLER
METHOD
a1=
Where, k=2,3,4,…
f(x)=0
Where,

6. Chebyshev Method
It is an iterative method for
determining the solutions for the
system of linear equations.
This method is named after Russian
mathematician ‘Pafnuty Chebyshev’.

7. FORMULA FOR CHEBYSHEV
METHOD

8. Fixed Point Iteration Method
It is a method for solving the equations
of the form f(x)=0 & this is transformed
to by making the initial guess of
x0,the approximations of x1,x2,… are
computed by iteration form.

9. FORMULAE FOR FIXED
POINT ITERATION METHOD

10. Aitken’s Delta Square Method
This is a series acceleration method
used for accelerating the rate of
convergence of a sequence.
This method is named after Alexander
Aitken.

11. FORMULAE FOR AITKEN’S
DELTA SQUARE METHOD

12. Birge Vieta Method
•Used for finding roots of polynomials
functions.
•It uses synthetic division of a
polynomial to extract factor of the
given polynomial in the form of (x-p).

13. FORMULA FOR BIRGE
VIETA METHOD

14. Bairstow Method
It is an efficient algorithm for finding
roots of real polynomial of arbitrary
degree.
 The algorithm find the roots in
complex conjugate pairs using only real
arithmetic.

15. FORMULAE FOR BAIRSTOW
METHOD
q
p
p p p
q qq q

16. Advantages Of Numerical Methods
 We can solve complex problems with simple
operations.
 In many problems , analytical methods fail,
in such cases numerical methods works out
to be very well.

17. Disadvantage Of Numerical
Methods
It gives approximate solutions but not
the exact solutions.

18. APPLICATIONS OF
NUMERICAL METHODS
 Weather Predictions
 Vehicles By Using Computer Simulation.
 Spacecrafts
 In private investment funds for calculating
stock values.
 In airlines for fixing air fares & fuel prices.
WEATHER
PREDICTIONS

19. Conclusions
 For finding roots & numerical optimization.
 We can estimate solutions for linear & non-
linear equations.

20. References
 www. Wiki pedia. com/numerical methods
 Numerical Methods by M.K. JAIN
 Applied Mathematics by Dr. B.S. GREWAL