Use the Jacobi method and Gauss-Seidel method to solve the following system until the L¹-norm of Ax is less than or equal to Tol = 1 × 10-4. Show the detailed calculation of the first 3 iterations of each method. 1 x₁ + 2x₂ + 3 1 5 == -X3 1 1 1 -X₁ 32 1 1 7*2+ 5*3= 1 31 4 ·X3=== 12 17 60

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
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Use the Jacobi method and Gauss-Seidel method to solve the following system until the L¹-norm of
Ax is less than or equal to Tol = 1 × 10-4. Show the detailed calculation of the first 3 iterations of each method.
1
x₁ + 2x₂ + 3
1 5
==
-X3
1
1
1
21 32
1
1
1
3³1+√³x₂ + 5*3=
4
·X3===
12
17
60
Transcribed Image Text:Use the Jacobi method and Gauss-Seidel method to solve the following system until the L¹-norm of Ax is less than or equal to Tol = 1 × 10-4. Show the detailed calculation of the first 3 iterations of each method. 1 x₁ + 2x₂ + 3 1 5 == -X3 1 1 1 21 32 1 1 1 3³1+√³x₂ + 5*3= 4 ·X3=== 12 17 60
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