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midterm2 - COT 3502 Computer Model Formulation Spring 2008...

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COT 3502 Computer Model Formulation Spring 2008 1 Midterm Exam 2 March 27, 2008, 1:50 pm to 3:50 pm Closed books, notes, and computers. Calculators should be used only for arithmetic calculations (not for plotting or analytical derivations). 1. (20 points) Consider the simple iteration method of solution of the following equation: x = g ( x ) , where g ( x ) = x 2 + 1 2 x - 1 2 . (1) The graph of function y = g ( x ) is shown below. -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 x y y=g(x) (a) (10 points) Check convergence of the simple iteration method to each of the roots of this equation. You may assume that initial conditions for the iterations are sufficiently close to the root. (b) (10 points) Estimate a range of initial conditions for the simple iteration method that would lead to convergence to each of the roots. You may use either graphical or analytical methods to answer these questions. Do not perform iterations numerically! You may also use the above plot if necessary. Make sure to clearly show your work!
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COT 3502 Computer Model Formulation Spring 2008 2 2. (20 points) Perform the LU-decomposition of the following matrix:
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