The linear system x 1 x 3 = 0.2, 1/2 x 1 + x 2

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The linear system x₁ − x₃ = 0.2, −1/2 x₁ + x₂ – 1/4 x₃ = −1.425, x₁ – 1/2 x₂ + x₃ = 2. Has the solution (0.9,−0.8, 0.7)^t .

a. Is the coefficient matrix

Strictly diagonally dominant?

b. Compute the spectral radius of the Gauss-Seidel matrix T_g.

c. Use the Gauss-Seidel iterative method to approximate the solution to the linear system with a tolerance of 10⁻² and a maximum of 300 iterations.

d. What happens in part (c) when the system is changed to x₁ − 2x₃ = 0.2, −1/2 x₁ + x₂ – 1/4 x₃ = −1.425, x₁ – 1/2 x₂ + x₃ = 2.

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Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

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Question Posted: Mar 22, 2016 02:57 AM

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The linear system x 1 x 3 = 0.2, 1/2 x 1 + x 2

Question:

1 -4 A = 1 1

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a A is not strictly diagonally dominant b Since T g is co...View the full answer

Numerical Analysis

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