3. Given the linear system x, +8x, + 2x, = -3 - 2x, +x2 +5x3 =7 %3D 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 | -).

3. Given the linear system x, +8x, + 2x, = -3 - 2x, +x2 +5x3 =7 %3D 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 | -).

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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A: Solution:

Question

take k as 1

(for example, a value is given as ?. ?? in the question would be
equal to ?. ? × ? = ?. ?)

3.
Given the linear system
X, +8x, + 2x, =-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 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.

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