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, . . . , O). 21. -4x, + 5x, = 1 22. 4.x, + 2.x, - 2.x, = 0 X, - 3x, - x, = 7 3x, - x2 + 4.x, = 5 X, + 2x, = 3

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, . . . , O). 21. -4x, + 5x, = 1 22. 4.x, + 2.x, - 2.x, = 0 X, - 3x, - x, = 7 3x, - x2 + 4.x, = 5 X, + 2x, = 3

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.5: Iterative Methods For Solving Linear Systems

Problem 19EQ

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