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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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..
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
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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