Given the linear system X, +8x, +2x3 = -3 - 2x, + x2 +5x3 =7 4x, + x, – x3 = 1 Use the Gauss-Seidel iterative method with X(®)=0.1k to approximate the solution. Compute 3 iterations and calculate ɛ, in each iteration using maximum magnitude norm (|| X||.). Hint: First, check whether the method is guaranteed to converge or not. If necessary, rearrange the order of equations to ensure convergence.
Given the linear system X, +8x, +2x3 = -3 - 2x, + x2 +5x3 =7 4x, + x, – x3 = 1 Use the Gauss-Seidel iterative method with X(®)=0.1k to approximate the solution. Compute 3 iterations and calculate ɛ, in each iteration using maximum magnitude norm (|| X||.). Hint: First, check whether the method is guaranteed to converge or not. If necessary, rearrange the order of equations to ensure convergence.
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
k=3
Transcribed Image Text:Given the linear system
X¡ +8x, +2x3 = -3
- 2x, +x2 +5x3 =7
4x, +x2 - x3 = 1
Use the Gauss-Seidel iterative method with X®)=0.1k to approximate the solution. Compute
3 iterations and calculate ɛa in each iteration using maximum magnitude norm (X).
Hint: First, check whether the method is guaranteed to converge or not. If necessary,
rearrange the order of equations to ensure convergence.
Transcribed Image Text:For the questions, take the value of kas the last digit of your student number. If the last digit of
your student number is 0, take k as 10. For example, for a student whose number is 04000375, as
the last digit of the student number is 5, k=5 and a value given as 0. 1k in the question would be
equal to 0.1 × 5 = 0. 5
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