To solve: The system starting from xo = [1 1 1] in three steps and up to 6S computation by Gauss- Seidel iteration. The approximation of the solution after three steps is x₁ = 6.39734, x2 = 3.6 and x3 = 1.119335. Calculation: The given equation is: 4x1-x2 = 22 -X1 +4x3 = -2.4 Rearrange the above equations is given below: x₁ = 0.25x2 +5.5 x2 = 0.25x3 + 3.35 x3 = 0.25x1 - 0.48 Using Gauss-Seidel iteration method to solve this system. x (m+1) 0.25x2 (m) +5.5 (m+1) x2 = 0.25x3 (m) +3.35 (m+1) = X3 - 0.48 4x2-x3 = 13.4 0.25x (m)
To solve: The system starting from xo = [1 1 1] in three steps and up to 6S computation by Gauss- Seidel iteration. The approximation of the solution after three steps is x₁ = 6.39734, x2 = 3.6 and x3 = 1.119335. Calculation: The given equation is: 4x1-x2 = 22 -X1 +4x3 = -2.4 Rearrange the above equations is given below: x₁ = 0.25x2 +5.5 x2 = 0.25x3 + 3.35 x3 = 0.25x1 - 0.48 Using Gauss-Seidel iteration method to solve this system. x (m+1) 0.25x2 (m) +5.5 (m+1) x2 = 0.25x3 (m) +3.35 (m+1) = X3 - 0.48 4x2-x3 = 13.4 0.25x (m)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
THIS IS EASY. PLEASE HELP.
Can someone help me how did the 0.25 values and the constant values were derived in the highlighted part? thank you so much.
![To solve: The system starting from Xo = [1 1 1] in three steps and up to 6S computation by Gauss-
Seidel iteration.
The approximation of the solution after three steps is x₁ = 6.39734, x2 = 3.6 and x3 = 1.119335.
Calculation:
The given equation is:
4x1-x2
= 22
4x2x3 = 13.4
-X1
+ 4x3
= -2.4
Rearrange the above equations is given below:
x₁ =
0.25x2
+ 5.5
x2 =
0.25x3 + 3.35
x3 = 0.25x1
- 0.48
Using Gauss-Seidel iteration method to solve this system.
Xy (m+1)
0.25x2 (m)
+5.5
X₂ (m+1) =
0.25x3(m)
+ 3.35
X3
- 0.48
(m+1) = 0.25x₁(m)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f2b504f-5266-495b-9ca8-0a62198e0e92%2F31c2ce7e-4fa3-4077-be60-305f59b7a024%2Fr92eh5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To solve: The system starting from Xo = [1 1 1] in three steps and up to 6S computation by Gauss-
Seidel iteration.
The approximation of the solution after three steps is x₁ = 6.39734, x2 = 3.6 and x3 = 1.119335.
Calculation:
The given equation is:
4x1-x2
= 22
4x2x3 = 13.4
-X1
+ 4x3
= -2.4
Rearrange the above equations is given below:
x₁ =
0.25x2
+ 5.5
x2 =
0.25x3 + 3.35
x3 = 0.25x1
- 0.48
Using Gauss-Seidel iteration method to solve this system.
Xy (m+1)
0.25x2 (m)
+5.5
X₂ (m+1) =
0.25x3(m)
+ 3.35
X3
- 0.48
(m+1) = 0.25x₁(m)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
