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Fall 2008_TEST _2

# Fall 2008_TEST _2 - TEST#2A PGE 310 Name Signature UT EID...

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TEST #2A (November 13, 2008) PGE 310 Name: Signature: UT EID: NOTES: 1. You have 1 hour and 15 minutes. Points will be deducted for tests turned in after 12:15 2. Write your name on all pages of the test 3. SHOW ALL WORK. Partial (or any credit) cannot be given for problems without work shown

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1. Qualitative Questions (30 points) (a) I want to solve some nonlinear equation f(x) = 0 using x=1 and x=2 as guess values. If the first 3 iterations of the Bisection and False-Position Method are given below, what would I get for “x” in the FIRST iteration of the Secant method? Iteration x_new (Bisection) x_new (False Position) ---------- --------------------- ------------------------ 1 1.5 1.6667 2 1.75 1.72727 3 1.875 1.7317 (b) Consider the non-linear function below; f(x)=0. Using an initial guess of x = -0.5 , On the curve, show GRAPHICALLY the first step of the Newton- Raphson method. -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 x f(x) (c) I have to solve a system of equations Ax=b several times (maybe hundreds). The matrix A never changes, but the vector b changes every time. Should I use Gauss Elimination or LU decomposition? Briefly explain (and be specific)
(d) Consider the following system of equations. As written, is convergence

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Fall 2008_TEST _2 - TEST#2A PGE 310 Name Signature UT EID...

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