Find the spectral radius of the jacobi and gauss-seidel

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Reference no: EM131252624

Consider the 2×2 matrix

and suppose we are required to solve Ax = b.

(a) Write down explicitly the iteration matrices corresponding to the Jacobi, Gauss-Seidel, and SOR schemes.

(b) Find the spectral radius of the Jacobi and Gauss-Seidel iteration matrices and the asymptotic rates of convergence for these two schemes.

(d) Find the optimal SOR parameter, ω∗. What is the spectral radius of the corresponding iteration matrix? Approximately how much faster would SOR with ω∗ converge compared to Jacobi?

Reference no: EM131252624

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