MAD4401Quiz1 - h,x 3 h Problem 3.2 In Problem 3.1...

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MAD 4401 Quiz 1 James Keesling 1 Bisection Method Problem 1.1. Determine a solution to cos( x ) = x using the Bisection Method. Problem 1.2. Determine the real roots of the polynomial p ( x ) = x 10 - 25 · x 5 + 10 · x - 15 using the Bisection Method. 2 Newton’s Method Problem 2.1. Approximate 6 5 using Newton’s Method. Problem 2.2. Determine a solution to cos( x ) = x using Newton’s Method. Problem 2.3. Determine the real roots of the polynomial p ( x ) = x 10 - 25 · x 5 + 10 · x - 15 using Newton’s Method. 3 Numerical Differentiation Problem 3.1. Determine a formula to estimate the second derivative of a function f ( x ) at the point x 0 using the points { x 0 - h,x 0 ,x 0 + 2 ·
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Unformatted text preview: h,x + 3 · h } . Problem 3.2. In Problem 3.1 determine the optimal h in estimating the second deriva-tive. Also determine the accuracy of the estimate assuming that the error in computing f ( x ) is approximately ± = 10-20 . 4 Lagrange Interpolating Polynomials Problem 4.1. Determine the Lagrange polynomial going through the following points { (-1 , 2) , (0 , 1) , (1 , 2) , ( 3 2 ,-1) , ( 5 2 , 0) } . Problem 4.2. For the data points in the previous problem determine the polynomials { L i ( x ) | i = 0 , 1 , 2 , 3 , 4 } . 1...
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This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.

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