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Why do we find the approximate solution?

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Old   February 7, 2007, 21:28
Default Why do we find the approximate solution?
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I have a silly question-

Why do we find out the approximate solutions in various numerical methods , when we already have the exact solution, with which we compare it in order to estimate the error?

Another question is-

What are 'a priori' and 'a posteriori' error? whats the difference between them?

I hope someone helps.

Thanks in anticipation. Meena
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Old   February 9, 2007, 11:04
Default Re: Why do we find the approximate solution?
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I have a silly answer:

For how many *real* problems of interest do exact solutions actually exist?

Also, 'a priori' = before analysis is performed, 'a posteriori' = afterwards. Nearly every error estimate I've ever seen is a posteriori.
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