Error in Numerical method

1. MATH 2331 - ERROR IN NUMERICAL
METHODS
Sourav Maiti
M tech, Electrical Engineering
BUDGE BUDGE INSTITUTE OF TECHNOLOGY

2. ERROR IN NUMERICAL METHODS
1. Definition
2. Type
3. Example

3. Definition:
The approximate representation of a real number
obviously differs from the actual number, whose
difference is called an error.
the difference between an observed or calculated value
and a true value.
The error in a computed quantity is defined as
Error = True Value - Approximate Value.

4. Type:
1. Absolute Error
2. Relative Error
3. Persentage Error

5. Absolute Error :
Absolute value of an error is called the absolute error.

6. Relative Error:
The relative error is a measure of the error in relation to the size
of the true value as given by
Relative Error= Error/True Value
Here, we assume that the true value is non-zero.

7. Persentage Error:
The percentage error is defined as Percentage
Error = 100 x Relative Error.

8. Example:
★ Let Xa denote the approximation to the real number x. We use the
following notations:
E(Xa)=: Erroг (Xa) =Xa-x
Ea(Xa)=: Absolute Error (Xa) =[E(Xa)]
Er(Xa)=: Relative Error(Xa)= E(Xa)/x , x≠0.
The absolute error has to be understood more carefully because a
relatively small difference between two large numbers can appear to
be large, and a relatively large difference between two small numbers
can appear to be small. On the other hand, the relative error gives a
percentage of the difference between two numbers, which is usually
more meaningful as illustrated below.

10. Thank You