Iterative - Week 12 Iterative solutions to systems of linear equations Iterative solutions 3x-z =2-x 2y =-1-4x 4y 8z=28 Solve for x,y,z x=(2 z/3

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Week 12 - Iterative solutions to systems of linear equations
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Iterative solutions 3x -z =2 -x +2y =-1 -4x+4y+8z=28 Solve for x,y,z: x= (2+z)/3 y= (-1+x)/2 z= (28+4x-4y)/8
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Iterative solutions x= (2+z)/3 y= (-1+x)/2 z= (28+4x-4y)/8 Use these from an initial guess to estimate the solution. x n = (2+z n-1 )/3 y n = (-1+x n-1 )/2 z n = (28+4x n-1 -4y n-1 )/8
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So where do we start? Iterative solutions Answer: Anywhere, closer just converges faster. I shall pick b 0 = [0, 0, 0]
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Iterative solutions x n = (2+z n-1 )/3 y n = (-1+x n-1 )/2 z n = (28+4x n-1 -4y n-1 )/8 b 0 = [0, 0, 0] b 1 : b 2 : x 2 = (2+z 1 )/3 y 2 = (-1+x 1 )/2 z 2 = (28+4x 1 -4y 1 )/8 x 1 = (2+z 0 )/3 y 1 = (-1+x 0 )/2 z 1 = (28+4x 0 -4y 0 )/8 b 1 = [2/3, -1/2, 28/8] b 2 = [1.83, -0.166, 4.083]
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Iterative solutions x n = (2+z n-1 )/3 y n = (-1+x n-1 )/2 z n = (28+4x n-1 -4y n-1 )/8 b 0 = [0, 0, 0] b 1 : x 1 = (2+z 0 )/3 y 1 = (-1+x 0 )/2 z 1 = (28+4x 0 -4y 0 )/8 b 1 = [2/3, -1/2, 28/8]
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x n = (2+z n-1 )/3 y n = (-1+x n-1 )/2 z n = (28+4x n-1 -4y
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This note was uploaded on 10/21/2011 for the course CSCI 2031 taught by Professor Meyer during the Spring '08 term at Minnesota.

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Iterative - Week 12 Iterative solutions to systems of linear equations Iterative solutions 3x-z =2-x 2y =-1-4x 4y 8z=28 Solve for x,y,z x=(2 z/3

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