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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##### Document information

Uploaded by:
pankarithi

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University:
Ankit Institute of Technology and Science

Subject:
Numerical Methods

Upload date:
17/04/2013