aking the initial approximation x = 0.75, x=-1.75 and x) = -0.25, apply three iterations of the Gauss-Seidel Method to the system. Vill the Jacobi and Gauss-Seidel iterates for all 3 x 3 linear systems that are not SDD always diverge? If not, give an example of a system that is not SDD, but for which the Jacobi and Gauss-Seidel iterates converge to the solution of the system.
aking the initial approximation x = 0.75, x=-1.75 and x) = -0.25, apply three iterations of the Gauss-Seidel Method to the system. Vill the Jacobi and Gauss-Seidel iterates for all 3 x 3 linear systems that are not SDD always diverge? If not, give an example of a system that is not SDD, but for which the Jacobi and Gauss-Seidel iterates converge to the solution of the system.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 10E
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Transcribed Image Text:The 3 x 3 system below has solution x₁ = 1, 2 = -2 and x3 = 0.
4x1 + 2x2 - 2x3 = 0
2x16x22x3
= 14
3x1x2 + 4x3 = 5
(0)
aking the initial approximation (0) = 0.75, x
three iterations of the Gauss-Seidel Method to the system.
(0)
= -1.75 and x = -0.25, apply
Vill the Jacobi and Gauss-Seidel iterates for all 3 x 3 linear systems that are not
SDD always diverge? If not, give an example of a system that is not SDD, but for which
the Jacobi and Gauss-Seidel iterates converge to the solution of the system.
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