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In Exercises 1– 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x,, x, · . . , x,) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. %3D 1. Зх, x2 = 2 2. - 4x, + 2x, = -6 X, + 4x, = 5 3. 2х, - х, 3x, - 5x, 1 %3D = 2 x¡ - 3x, + x = -2 -X, + x2 - 3x3 = -6 4. 4x, + x2 + X3 = X - 7x, + 2r, = -2 3x 7 %3D %3D + 4x3 = 11

In Exercises 1– 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x,, x, · . . , x,) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. %3D 1. Зх, x2 = 2 2. - 4x, + 2x, = -6 X, + 4x, = 5 3. 2х, - х, 3x, - 5x, 1 %3D = 2 x¡ - 3x, + x = -2 -X, + x2 - 3x3 = -6 4. 4x, + x2 + X3 = X - 7x, + 2r, = -2 3x 7 %3D %3D + 4x3 = 11

Linear Algebra: A Modern Introduction
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 25EQ
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8:39 O V A • Bllll 68%i In Exercises 1– 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x, X2, . . . , X„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. Зх, — х, %3D 2 2. - 4x, + 2x, = -6 x, + 4x, = 5 Зх, — 5х, — 1 3. 2х, — х, 4. 4x, + x, + x3 = 7 = x1 - 3x, + xz = -2 -x, + x, - 3x = -6 x - 7x, + 2x; = -2 3x, + 4x3 = 11 5. Apply the Gauss-Seidel method to Exercise 1. 6. Apply the Gauss-Seidel method to Exercise 2. 7. Apply the Gauss-Seidel method to Exercise 3. 8. Apply the Gauss-Seidel method to Exercise 4.
Transcribed Image Text:8:39 O V A • Bllll 68%i In Exercises 1– 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x, X2, . . . , X„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. Зх, — х, %3D 2 2. - 4x, + 2x, = -6 x, + 4x, = 5 Зх, — 5х, — 1 3. 2х, — х, 4. 4x, + x, + x3 = 7 = x1 - 3x, + xz = -2 -x, + x, - 3x = -6 x - 7x, + 2x; = -2 3x, + 4x3 = 11 5. Apply the Gauss-Seidel method to Exercise 1. 6. Apply the Gauss-Seidel method to Exercise 2. 7. Apply the Gauss-Seidel method to Exercise 3. 8. Apply the Gauss-Seidel method to Exercise 4.
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