Consider the linear system 5x1 X2 + X3 = 2 2а1 + 822 — 2аз 8. x1 - 3x2 + 9x3 = 9 and let x0) be any initial guess. Select all statements that are true. O (k+1) 1 1 (k+1) (k+1) 3* + 2, k = 0,1, 2, ... for the Gauss-Seidel Iteration. The iteration matrix T' for the Jacobi iteration is given by 1/5 -1/5] T = -1/4 1/4 -1/9 1/3 Both the Jacobi and the Gauss-Seidel Iteration diverge. The Gauss-Seidel iteration converges to the exact solution of Ax =b while the Jacobi iteration doesn't. Both the Jacobi and the Gauss-Seidel Iteration do not converge to the exact solution of Ax = b.
Consider the linear system 5x1 X2 + X3 = 2 2а1 + 822 — 2аз 8. x1 - 3x2 + 9x3 = 9 and let x0) be any initial guess. Select all statements that are true. O (k+1) 1 1 (k+1) (k+1) 3* + 2, k = 0,1, 2, ... for the Gauss-Seidel Iteration. The iteration matrix T' for the Jacobi iteration is given by 1/5 -1/5] T = -1/4 1/4 -1/9 1/3 Both the Jacobi and the Gauss-Seidel Iteration diverge. The Gauss-Seidel iteration converges to the exact solution of Ax =b while the Jacobi iteration doesn't. Both the Jacobi and the Gauss-Seidel Iteration do not converge to the exact solution of Ax = b.
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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![Consider the linear system
5x1
X2 +
X3 = 2
2а1 + 822 — 2аз
8.
x1
- 3x2 + 9x3
= 9
and let x0) be any initial guess. Select all statements that are true.
O (k+1)
1
1
(k+1)
(k+1)
3*
+ 2, k = 0,1, 2, ... for the Gauss-Seidel
Iteration.
The iteration matrix T' for the Jacobi iteration is given by
1/5
-1/5]
T =
-1/4
1/4
-1/9 1/3
Both the Jacobi and the Gauss-Seidel Iteration diverge.
The Gauss-Seidel iteration converges to the exact solution of Ax = b while the Jacobi
iteration doesn't.
Both the Jacobi and the Gauss-Seidel Iteration do not converge to the exact solution of
Ax = b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa93f86ee-0c47-4566-900d-096238a0262e%2Faea49967-b945-4087-ab59-09f3b33abe3c%2Ftkbb4ib_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the linear system
5x1
X2 +
X3 = 2
2а1 + 822 — 2аз
8.
x1
- 3x2 + 9x3
= 9
and let x0) be any initial guess. Select all statements that are true.
O (k+1)
1
1
(k+1)
(k+1)
3*
+ 2, k = 0,1, 2, ... for the Gauss-Seidel
Iteration.
The iteration matrix T' for the Jacobi iteration is given by
1/5
-1/5]
T =
-1/4
1/4
-1/9 1/3
Both the Jacobi and the Gauss-Seidel Iteration diverge.
The Gauss-Seidel iteration converges to the exact solution of Ax = b while the Jacobi
iteration doesn't.
Both the Jacobi and the Gauss-Seidel Iteration do not converge to the exact solution of
Ax = b.
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