ERROR AND COMPUTER ARITHMETIC
ERROR AND THEIR ANALYSIS
SOURCES OF ERROR :
Following are the board sources of error in numerical analysis .
1) INPUT ERROR
The input information is rarely exact since it comes from the experiments and any experiment can give result of only limited accuracy.
Moreover the quality used can be represented in a computer for only a limited number of digits .
2) ALGORITHMIC ERRORS.
If direct algorithm based on a finite sequence of operations are used, error due to limited step don't amplify the existing errors, but if infinite algorithm are used , exact results are expected only after a infinite number of steps .
As this be done in practice , the algorithm has to be stopped after a finite number of steps and the results are not exact.
3) COMPUTATIONAL ERRORS.
Even When elementary operations such as multiplication and division are used, the number of digits increases greatly so that the results cannot be held fully in a register available in a given computer
In such cases , a certain number of digits must be discarded . Furthermore ,the error here accumulate one after another from from operation to operation, changing during the process and producing new errors.
the following
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