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PGE 310 - HW 9

# PGE 310 - HW 9 - The University of Texas at Austin Fall...

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Fall 2011 - PGE 310: Formulation and Solution in Geosystems Engineering HW #9: System of Linear Equations by Iterative Methods - System of Non-Linear Equations by Newton’s Method Due Date: Thursday Nov 10 th 2011 Do NOT forget to follow the guideline for submitting homework (Attached to the end of this file) 1. System of Linear Equations – Iterative Methods (By HAND) Assume that in your Static Exam, you are asked to figure out the support forces of the structure below. ( ? ?, ?, 3 2 1 F F F ) After writing the force and the moment equilibrium equations, you ended up with the following system of linear equations: 10 6 2 6 4 2 13 3 5 3 2 1 3 2 1 3 2 1 F F F F F F F F F a) Determine if the coefficient matrix of this system is diagonally dominant, so that the convergence of iterative methods is guaranteed. b) Determine l 1 -matrix norm , l 2 -matrix norm and l -matrix norm of the coefficient matrix. c) Determine the condition number of the coefficient matrix. How many digits of precision will be lost in solving this system of equations? d) Solve the system of equations for 3 2 1 , F and F F using the initial guess 0 0 0 3 2 1 ) 0 ( F F F F using the following methods: 1. Richardson Iteration using Q=I 2. Jacobi Method 3. Gauss-Seidel Method 4. SOR (Successive Over Relaxation) Method with 2 . 1 - Determine only the first two iterations, i.e. ) 2

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PGE 310 - HW 9 - The University of Texas at Austin Fall...

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