In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x₁, x₂,...,x) = (0, 0,..., 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x₁ x₂ = 2 x₁ + 4x₂ = 5 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1 3. 2x₁ - x₂ 4. 4x₁ + x₂ + x3 7 = x₁ = 3x₂ + x3 = -2 x₁ - 7x₂ + 2x3 2 + 4x3 = = 3x₁ = -x₁ + x₂-3x3 -6 11 5. Apply the Gauss-Seidel method to Exercise 1. 11
In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x₁, x₂,...,x) = (0, 0,..., 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x₁ x₂ = 2 x₁ + 4x₂ = 5 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1 3. 2x₁ - x₂ 4. 4x₁ + x₂ + x3 7 = x₁ = 3x₂ + x3 = -2 x₁ - 7x₂ + 2x3 2 + 4x3 = = 3x₁ = -x₁ + x₂-3x3 -6 11 5. Apply the Gauss-Seidel method to Exercise 1. 11
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 6EQ
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