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Unformatted text preview: C/N r for some constant C when N is large. Hint: If I-E N ≈ C/N r then E 2 N-E N ≈ C (1-2-r ) /N r 1 and so E 2 N-E N E 4 N-E 2 N ≈ 2 r or r ≈ log 2 ± E 2 N-E N E 4 N-E 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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This note was uploaded on 10/26/2010 for the course ENGINEERIN MECH221 taught by Professor Wetton during the Spring '10 term at The University of British Columbia.
- Spring '10