Differentiation

Differentiation - length of the mantissa). Analyze these...

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Homework Let f ( t ) = sin ( t ). Define finite difference D h ( a ) = f ( a + h ) - f ( a ) h . Let a = 1. Compute experimentally the total error e h ( a ) = | D h ( a ) - f 0 ( a ) | for h i = 10 - i ,i = 1 ,..., 16. Tabulate and plot these values. Note that this total error is a sum of the discretization error (consequence of replacing derivative by finite difference) and round off error (due to final
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Unformatted text preview: length of the mantissa). Analyze these two inuences as a function of h (note that | f 00 ( x ) | 1), estimate the value of h opt and compare it with the results of the experiments....
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