# Propagation of Errors - Numerical Methods - Lecture Slides, Slides for Numerical Methods. Ankit Institute of Technology and Science

## Numerical Methods

Description: The main points are: Propagation of Errors, Numerical Methods, Maximum Possible Value, Errors in Formulas, Axial Member, Formula for Error Propagation, Subtraction of Numbers, Objective Function, Vector Operator, Initial Guess of Root
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Propagation of Errors
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Propagation of Errors
In numerical methods, the calculations are not
made with exact numbers. How do these
inaccuracies propagate through the calculations?
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Example 1:
Find the bounds for the propagation in adding two numbers. For example if one
is calculating X +Y where
X = 1.5 ± 0.05
Y = 3.4 ± 0.04
Solution
Maximum possible value of X = 1.55 and Y = 3.44
Maximum possible value of X + Y = 1.55 + 3.44 = 4.99
Minimum possible value of X = 1.45 and Y = 3.36.
Minimum possible value of X + Y = 1.45 + 3.36 = 4.81
Hence
4.81 ≤ X + Y ≤4.99.
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Propagation of Errors In Formulas
f
nn XXXXX ,,.......,,, 1321
f
n
n
n
n
X
X
f
X
X
f
X
X
f
X
X
f
f
+
++
+
1
1
2
2
1
1
.......
If is a function of several variables
then the maximum possible value of the error in is
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