ma174_hw5

ma174_hw5 - Assigned Friday Oct 21 2011 Due Date Friday Oct...

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Unformatted text preview: Assigned: Friday Oct. 21, 2011 Due Date: Friday Oct. 28, 2011 MATH 174/274: Homework V ”Iterative Methods for Linear and Nonlinear Systems” Fall 2011 1. Consider the following 3 × 3 system: 4 x 1- x 2 + x 3 = 7 4 x 1- 8 x 2 + x 3 =- 21- 2 x 1 + x 2 + 5 x 3 = 15 . The actual solution to the system is ~x = (2 , 4 , 3) T . (a) Write down the Jacobi iteration formula for the above system. (b) Using the initial guess ~x (0) = (0 , , 0) T , compute the first four Jacobi iterations for the above system as well as the error k ~x- ~x ( i ) k ∞ for each iterate ( NOTE: feel free to use your calculator or MATLAB for this, but make sure to report enough significant digits ). Display the data in a table of the form: i 1 2 3 4 x i 1 x i 2 x i 3 k ~x- ~x ( i ) k ∞ (c) Determine the Gauss-Seidel iterate for the above system. (d) Repeat part (b) using the Gauss-Seidel iterate from part (c). Display the data in a table of the form: 1 Assigned: Friday Oct. 21, 2011 Due Date: Friday Oct. 28, 2011Friday Oct....
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ma174_hw5 - Assigned Friday Oct 21 2011 Due Date Friday Oct...

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