3. Given the linear system X1 +8.x, +2x3 = -3 - 2x, + x2 + 5x3 = 7 4x1 +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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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take k as 1

Given the linear system
X1 +8x, +2x3 = -3
- 2x, + x2 + 5x3 =7
4.x1 + x2 - x3 = 1
Use the Gauss-Seidel iterative method with XO=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.
3.
Transcribed Image Text:Given the linear system X1 +8x, +2x3 = -3 - 2x, + x2 + 5x3 =7 4.x1 + x2 - x3 = 1 Use the Gauss-Seidel iterative method with XO=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. 3.
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