Study the convergence of the Jacobi and the Gauss-Seidel method for the following systems bystarting with aro (0,0,0)T and performing three iterations:(i)5r1+2r2 + r3 0.12, 1.75r +7r2+ 0.5r3 0.1, rı + 0.2r2 +4.5.r3 0.5.(ii)r1 -2r2 + 2r3 1, -rı + r2-r3 1, - 2r1-2r2+ r3 1.

1 Given: 5x1+2x2+x3=0.12 ⋯11.75x1+7x2+0.5x3=0.1 ⋯2x1+0.2x2+4.5x3=0.5 ⋯3 For Jacobi's method:…

Study the convergence of the Jacobi and the Gauss-Seidel method for the following systems by starting with ro (0,0,0)T and performing three iterations: (i)5r1 + 2r2 + r3 0.12, 1.75x+7r2+0.5r3 0.1, r1 + 0.2r2+4.5r3 = 0.5. (ii)r1-2r2+ 23 1, -r + r2-3 1, -2r1-22+r3 1.

Study the convergence of the Jacobi and the Gauss-Seidel method for the following systems by starting with ro (0,0,0)T and performing three iterations: (i)5r1 + 2r2 + r3 0.12, 1.75x+7r2+0.5r3 0.1, r1 + 0.2r2+4.5r3 = 0.5. (ii)r1-2r2+ 23 1, -r + r2-3 1, -2r1-22+r3 1.

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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Question

Study the convergence of the Jacobi and the Gauss-Seidel method for the following systems by
starting with aro (0,0,0)T and performing three iterations:
(i)5r1+2r2 + r3 0.12, 1.75r +7r2+ 0.5r3 0.1, rı + 0.2r2 +4.5.r3 0.5.
(ii)r1 -2r2 + 2r3 1, -rı + r2-r3 1, - 2r1-2r2+ r3 1.

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