In Exercises 21 and 22, the coefficient matrix of the system of linear equations is not strictly diagonally dominant. Show that the Jacobi and Gauss-Seidel methods converge using an initial approximation of (x, x2, . . . , x,) = (0, 0, . . . , 0). 21. -4x, + 5x, = 1 X, + 2x, = 3 22. 4.x, + 2.x, - 2.x, = 0 X, - 3x, - x, = 7 3x, - x2 + 4.x, = 5
In Exercises 21 and 22, the coefficient matrix of the system of linear equations is not strictly diagonally dominant. Show that the Jacobi and Gauss-Seidel methods converge using an initial approximation of (x, x2, . . . , x,) = (0, 0, . . . , 0). 21. -4x, + 5x, = 1 X, + 2x, = 3 22. 4.x, + 2.x, - 2.x, = 0 X, - 3x, - x, = 7 3x, - x2 + 4.x, = 5
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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Please answer number 22 with complete solution.
Transcribed Image Text:In Exercises 21 and 22, the coefficient matrix of the system of linear
equations is not strictly diagonally dominant. Show that the Jacobi
and Gauss-Seidel methods converge using an initial approximation
of (x1, x2, . . . , x,) = (0, 0, . . . , 0).
21. -4x, + 5x, = 1
X, + 2x, = 3
22. 4.x, + 2x, - 2.x, = 0
X, - 3x, - x, = 7
3x, - x2 + 4.x, = 5
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