11.15 Of the following three sets of linear equations, identify the set(s) that you could not solve using an iterative method such as Gauss-Seidel. Show using any number of iterations that is neces- sary that your solution does not converge. Clearly state your con- vergence criteria (how you know it is not converging). Set One Set Two Set Three 8x + 3y + z = 12 x + y + 5z = 7 -6x + 7z = 1 2x + 4y - z = 5 -x + 3y + 5z = 7 x + 4y - z = 4 -2x + 4y - 5z = -3 2y - z = 1 3x + y - z = 4

11.15 Of the following three sets of linear equations, identify the set(s) that you could not solve using an iterative method such as Gauss-Seidel. Show using any number of iterations that is neces- sary that your solution does not converge. Clearly state your con- vergence criteria (how you know it is not converging). Set One Set Two Set Three 8x + 3y + z = 12 x + y + 5z = 7 -6x + 7z = 1 2x + 4y - z = 5 -x + 3y + 5z = 7 x + 4y - z = 4 -2x + 4y - 5z = -3 2y - z = 1 3x + y - z = 4

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

100%

11.15 Of the following three sets of linear equations, identify the
set(s) that you could not solve using an iterative method such as
Gauss-Seidel. Show using any number of iterations that is neces-
sary that your solution does not converge. Clearly state your con-
vergence criteria (how you know it is not converging).
Set One
Set Two
Set Three
8x + 3y + z = 12 x + y + 5z = 7
-6x + 7z = 1
2x + 4y - z = 5
-x + 3y + 5z = 7
x + 4y - z = 4 -2x + 4y - 5z = -3
2y - z = 1
3x + y - z = 4

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