Improving accuracy of computation

Asked by Mear on 7 Sep 2011

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I'm doing an assignment for a class in numerical computation which involves calculating pi with a given formula. No problem there, however I'm also asked to improve accuracy by rewriting said formula.

I have to admit I have no idea what affects accuracy in matlab, especially when it's something as seemingly simple sa rewriting a relatively uncomplicated formula.

I'm wondering if anyone has any tips or examples for me, to help me understand how I can approach this. I haven't bothered posting the formula, since I'm really not after anyone giving me the solution, but rather understanding the question. :)

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Answer by Titus Edelhofer on 7 Sep 2011

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Most often numerical accuracy is (badly) affected when subtracting values of similar size. Example (using 4 digits only):

x1 = 1.234

x2 = 1.223

x = x1-x2 = 0.011

So: two numbers with 4 digits accuracy lead to a x with only two digits. Increasing accuracy is possible in those cases, where rearranging the formula leads to expressions avoiding the problem above....

Titus

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Answer by Nirmal Gunaseelan on 7 Sep 2011

I recommend reading Loren's post on this topic and might help you get a basic understanding of issues that you might want to be aware of. Also, kudos on taking particular effort in not posting an assignment question and asking the underlying question.

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