# hw10 - Homework 10 Math 471 Fall 2007 Assigned Thursday Due...

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Homework 10 Math 471, Fall 2007 Assigned: Thursday, November 19, 2007 Due: Thursday, November 30, 2007 Include a cover page Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Piecewise Linear Interpolation) Use the error theorem on p. 390 to compute an upper bound on the pointwise error from interpolating f ( x ) = e - x 2 on the interval [ - 4 , 4] with piecewise linear functions at the points - 4, - 2, 0, 2, and 4. (2) (Cubic Spline Interpolation) P. 403 #10, P. 404 #15 (3) (Richardson Extrapolation) P. 454 #11 (4) (Newton–Cotes). Suppose that f is a function with four continuous derivatives on the interval [ a, b ]. Recall that the error bound for the composite trapezoidal rule T ( h ) with panel width h is T ( h ) - Z b a f ( x ) d x = ( b - a ) h 2 12 f 00 ( ξ ) for some ξ [ a, b ]. The error in the composite Simpson’s rule S ( h ) with panel width h is S ( h ) - Z b a f ( x ) d x = ( b - a ) h 4 180 f (4) ( ξ ) for some (different) ξ [ a, b ].

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