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Unformatted text preview: C/N r for some constant C when N is large. Hint: If IE N ≈ C/N r then E 2 NE N ≈ C (12r ) /N r 1 and so E 2 NE N E 4 NE 2 N ≈ 2 r or r ≈ log 2 ± E 2 NE N E 4 NE 2 N ² . Use this last expression to estimate r . (b) Use an appropriate Richardson Extrapolation to get more accurate estimates of I . 3. Suppose that linear interpolation S ( x ) is used to estimate f ( x ) in the interval [0 ,h ] using the values f (0) and f ( h ). Derive an error bound for this interpolation of the form  f ( x )S ( x )  ≤ CK 2 h 2 for all x in [0 ,h ] where K 2 is the maximum of f (2) on the interval and C is a constant you must determine. Hint: modify the argument I showed in class for the error bound for tangent line approximation. 2...
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 Spring '10
 WETTON
 Numerical Analysis, Math Suggested Problems, Brian Wetton

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