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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
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.
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
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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