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Question 3: Solve the system of linear using Gauss Seidel iteration until maxx) – x"| <0.005 Therefore, 9 5.4 -1.98 (0 -3 -6.9 1.8 1.95 1 -2.8 x 0.82 9 5.4 -1.98 2 -5.1 -1.89 1.387 Step 2: Write down Gauss Seidel iteration formula -1.98-5.4x Solution: Step 1: Rearrange so that matrix A is diagonally dominant. l0l<|-3|+|-6,9|+|1.8|| 10|0|+1\+|-2.8| 9 (0 -3 -6.9 1.8 fe) _ 1.387– 2x**) +1.89x,) 1 -2.8 -5.1 9 5.4 1.95+3x*) –1.8 2 -5.1 -1.89 10|</2\+l-5.1|+|-1.89| -6.9 - 0.82 – Lxe+1) -2.8 Step 3: Take initial guess =(0,.o)" Step 4: Iterate using Gauss-Scidel itcration formula until max <0.005 k x1 x2 x3 x4 el e2 e3 c4 max error -0.2720 0.2200 0.2720 0.2929 0.2929 -0.2200 2 1 -0.2826 -0.2929 0.2826 456

Question 3: Solve the system of linear using Gauss Seidel iteration until maxx) – x"| <0.005 Therefore, 9 5.4 -1.98 (0 -3 -6.9 1.8 1.95 1 -2.8 x 0.82 9 5.4 -1.98 2 -5.1 -1.89 1.387 Step 2: Write down Gauss Seidel iteration formula -1.98-5.4x Solution: Step 1: Rearrange so that matrix A is diagonally dominant. l0l<|-3|+|-6,9|+|1.8|| 10|0|+1\+|-2.8| 9 (0 -3 -6.9 1.8 fe) _ 1.387– 2x**) +1.89x,) 1 -2.8 -5.1 9 5.4 1.95+3x*) –1.8 2 -5.1 -1.89 10|</2\+l-5.1|+|-1.89| -6.9 - 0.82 – Lxe+1) -2.8 Step 3: Take initial guess =(0,.o)" Step 4: Iterate using Gauss-Scidel itcration formula until max <0.005 k x1 x2 x3 x4 el e2 e3 c4 max error -0.2720 0.2200 0.2720 0.2929 0.2929 -0.2200 2 1 -0.2826 -0.2929 0.2826 456

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 48EQ
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Question 3: Therefore, Solve the system of linear using Gauss Seidel iteration until max <0.005 9 5.4 (-1,98) -3 -6.9 1.8 1.95 1 -2.8 0.82 9 5.4 -1.98 2 -5.1 -1.89 (1.387 Step 2: Write down Gauss Seidel iteration formula -1.98–5.4x) Solution: Step 1: Rearrange so that matrix A is diagonally dominant. l01</-3|+|-6,9|+|1.8|| l0|</0\+ \4\+|-2.8| (0 -3 -6.9 1.8 1.387– 2x*) +1.89x %3D 1 -2.8 -5.1 9 5.4 1.95+3x+) -1.8x 2 -5.1 -1.89 l01</2\+I-s.1|+|-1.89| -6.9 0.82 -1*+ -2.8 Step 3: Take initial guess x = (0,...0)' Step 4: Iterate using Gauss-Seidel iteration formula until max <0.005 k x1 x2 x3 x4 el c2 e3 e4 max error 1 -0.2200 -0.2720 -0.2826 -0.2929 0.2200 0.2720 0.2826 0.2929 0.2929 5
Transcribed Image Text:Question 3: Therefore, Solve the system of linear using Gauss Seidel iteration until max <0.005 9 5.4 (-1,98) -3 -6.9 1.8 1.95 1 -2.8 0.82 9 5.4 -1.98 2 -5.1 -1.89 (1.387 Step 2: Write down Gauss Seidel iteration formula -1.98–5.4x) Solution: Step 1: Rearrange so that matrix A is diagonally dominant. l01</-3|+|-6,9|+|1.8|| l0|</0\+ \4\+|-2.8| (0 -3 -6.9 1.8 1.387– 2x*) +1.89x %3D 1 -2.8 -5.1 9 5.4 1.95+3x+) -1.8x 2 -5.1 -1.89 l01</2\+I-s.1|+|-1.89| -6.9 0.82 -1*+ -2.8 Step 3: Take initial guess x = (0,...0)' Step 4: Iterate using Gauss-Seidel iteration formula until max <0.005 k x1 x2 x3 x4 el c2 e3 e4 max error 1 -0.2200 -0.2720 -0.2826 -0.2929 0.2200 0.2720 0.2826 0.2929 0.2929 5
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