9.3 - Math 2940 Solutions, Fall 2011 Section 9.3 3) I − A...

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Unformatted text preview: Math 2940 Solutions, Fall 2011 Section 9.3 3) I − A = −1 1 1 −1 7) In Gauss-Seidel S −1 has −2 as an eigenvector. Since | − 2| > 1 the iteration diverges. T= Here |λmax | = 1/9. For Jacobi, S −1 T= 30 03 30 −1 3 −1 −1 01 10 01 00 = = 1/3 0 1/3 0 1/3 0 1/9 1/3 01 00 = 0 1/3 . 0 1/9 so |λmax | = 1/3. 2 −1 1 2 2 −1 2 5 = . Then u2 = = and −1 2 0 −1 −1 2 −1 −4 2 −1 5 14 u3 = = . −1 2 −4 −13 The eigenvalues of our matrix are 1 and 3. An eigenvector for the larger eigenvalue is 1 . That is the direction to which we are converging. −1 16) u1 = ...
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This note was uploaded on 01/02/2012 for the course MATH 2940 at Cornell University (Engineering School).

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