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Given the following systems, 4x1 + 2x2 - x3 = 10 x1 + 3x2 - 2x3 = 4 2x1 - 2x2 + 3x3 = 6 1. Solve the system using Jacobi Method up to 11 iterations. This is the example that might help..

Given the following systems, 4x1 + 2x2 - x3 = 10 x1 + 3x2 - 2x3 = 4 2x1 - 2x2 + 3x3 = 6 1. Solve the system using Jacobi Method up to 11 iterations. This is the example that might help..

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer the following and show solutions.

Given the following systems,
4x1 + 2x2 - x3 = 10
x1 + 3x2 - 2x3 = 4
2x1 - 2x2 + 3x3 = 6

1. Solve the system using Jacobi Method up to 11 iterations.

This is the example that might help..

 

 

3RD ITERATION: x₂ = 3-√₂+² 2 = 3-1 + 1.1875 3 3 Yo = 7-2x₂-2₂ - 2x2-2₂ 7-210-757-1-1875 4 4 1.078125 Z₂ 2 4-x₂+x2= 4 -(0-75) +1 1.0625 4 ។ Iteration Y Z O 1 1.75 1 0.75 1 1-1875 1.0625 1.078125 1.0625 0.9947921 0.953125 1.003906 5 6 1.016927 1-001628 0-989583 0-995985 | 0.994141 0.996175 1.00303 0.999539 1-000678 As required, the difference of the last iteration Shoulder be less than 0.005, | X=1; y = 1 ; 2=1 L 2 3 4 (1 O 5 decimal O = 1.0625
Transcribed Image Text:3RD ITERATION: x₂ = 3-√₂+² 2 = 3-1 + 1.1875 3 3 Yo = 7-2x₂-2₂ - 2x2-2₂ 7-210-757-1-1875 4 4 1.078125 Z₂ 2 4-x₂+x2= 4 -(0-75) +1 1.0625 4 ។ Iteration Y Z O 1 1.75 1 0.75 1 1-1875 1.0625 1.078125 1.0625 0.9947921 0.953125 1.003906 5 6 1.016927 1-001628 0-989583 0-995985 | 0.994141 0.996175 1.00303 0.999539 1-000678 As required, the difference of the last iteration Shoulder be less than 0.005, | X=1; y = 1 ; 2=1 L 2 3 4 (1 O 5 decimal O = 1.0625
System of Linear Equations (Iterative Methods) Iterative methods are based on successive improvement of initial guesses for the solution. ITERATIVE METHODI: JACOBI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknowns of zero. Step 3. Perform iteration until the values of the unknown don't diverge anymore. folut Example & 肉丸 3x+2y2=3 4y+z=7 X-y + 4z = 4 Solution: NAA x = 3-y+z 3 Y = 7-2x-z 4 Z= 4-x+x 4 1st Iteration : x=0; y=0,2 = 0 X, = 3-ото = 1 Y₁ = 7-2(0) - (0) = 1.75 2,4-04 으 = 1 4 2ND ITERATION: x₂ = 3-y₁ +2₁= 3 ~ 1.75 +1 = 0.75 3 3 Y2:7-2x, 7,7-20)-(1 4 4 Z₂ = 4-X₁tY₁ = 4-1+1.75 4 4 = 1.1875
Transcribed Image Text:System of Linear Equations (Iterative Methods) Iterative methods are based on successive improvement of initial guesses for the solution. ITERATIVE METHODI: JACOBI METHOD Step 1. Rewrite the system Step 2. Initialize a value for the unknowns of zero. Step 3. Perform iteration until the values of the unknown don't diverge anymore. folut Example & 肉丸 3x+2y2=3 4y+z=7 X-y + 4z = 4 Solution: NAA x = 3-y+z 3 Y = 7-2x-z 4 Z= 4-x+x 4 1st Iteration : x=0; y=0,2 = 0 X, = 3-ото = 1 Y₁ = 7-2(0) - (0) = 1.75 2,4-04 으 = 1 4 2ND ITERATION: x₂ = 3-y₁ +2₁= 3 ~ 1.75 +1 = 0.75 3 3 Y2:7-2x, 7,7-20)-(1 4 4 Z₂ = 4-X₁tY₁ = 4-1+1.75 4 4 = 1.1875
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