# Hw5 - Homework#5 1 Perform three iterations of Jacobi method with starting guess x(0 =[0 0 0]t for the linear system 2 3 1 1 x 1 y = 0 0 2 10 2 2 5

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Homework #5 1. Perform three iterations of Jacobi method with starting guess ~x (0) = [0 , 0 , 0] t for the linear system 3 1 - 1 0 - 2 1 2 - 2 5 x y z = 2 0 10 . 2. (a) Write down the ﬁxed point problem ~x = C~x + ~ d solved by Jacobi method for the linear system of equations ± 10 1 1 - 1 ²± x y ² = ± 5 - 7 ² . (b) Find the eigenvalues of C by hand (they are complex). Will the Jacobi method converge in this case? Also, how does the speed of convergence compare to an order 1 method with asympototic error constant 1 / 2? 3. Perform two iterations of the Gauss-Seidel method with starting guess ~x (0) = [0 , 0 , 0] t for the linear system 3 1 - 1 0 - 2 1 2 - 2 5 x y z = 2 0 10 . 4. (a) Write down the ﬁxed point problem ~x = C~x + ~ d solved by the Gauss-Seidel method for the linear system of equations ± 10 1 1 - 1 ²± x y ² = ± 5 - 7 ² . (b) Find the eigenvalues of

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## This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.

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Hw5 - Homework#5 1 Perform three iterations of Jacobi method with starting guess x(0 =[0 0 0]t for the linear system 2 3 1 1 x 1 y = 0 0 2 10 2 2 5

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