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# hw16 - error at step n where n is the iteration number(Note...

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MAE 107 Assignment 6 Study Problems Only. Do not hand in. Epperson, Section 3.9 problem: 4. Epperson, Section 3.10 problem: 10. Epperson, Section 4.1 problems: 1, 2, 3, 9, 10. (Keep in mind that one uses Lagrange interpolation for these.) Epperson, Section 4.2 problems: 1, 2a, 2b, 15. Epperson, Section 4.7 problems: 1, 3. (Also do these with piecewise linear interpolation.) Find a root of f ( x ) = xe x - ( x 2 + 1) using both the methods given in (3.44) and (3.45) of Epperson, starting from x 0 = 1. Also use Newton’s method. Plot the log of the error at step n + 1 versus the log of the
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Unformatted text preview: error at step n , where n is the iteration number. (Note that you can use the ±nal iteration as the true solution.) What do the slopes look like? How does this compare with your expectation? (Don’t worry about small deviations from your expectation.) Also try starting from x = 2. What happens in that case? • Do the same thing as in Problem 15 of Section 4.2, but for the cases of f ( x ) = e-8 x 2 and f ( x ) = [1 + 25 x 2 ]-1 . Plot the original functions and the resulting polynomial interpolations over [-1 . 1 , 1 . 1]. 1...
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