Lecture 24 - Chapter 11 Iterative Methods for System of...

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Chapter 11 Iterative Methods for System of Equations
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Iterative Methods for Solving Matrix Equations 0 C , d Cx x b Ax ii = + = = Jacobi method Gauss-Seidel Method* Successive Over Relaxation (SOR) MATLAB’s Methods
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Iterative Methods = + + + = + + + = + + + = + + + 4 4 44 3 43 2 42 1 41 3 4 34 3 33 2 32 1 31 2 4 24 3 23 2 22 1 21 1 4 14 3 13 2 12 1 11 b x a x a x a x a b x a x a x a x a b x a x a x a x a b x a x a x a x a - - - = - - - = - - - = - - - = 44 3 43 2 42 1 41 4 4 33 4 34 2 32 1 31 3 3 22 4 24 3 23 1 21 2 2 11 4 14 3 13 2 12 1 1 a / ) x a x a x a b ( x a / ) x a x a x a b ( x a / ) x a x a x a b ( x a / ) x a x a x a b ( x Can be converted to
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Idea behind iterative methods: Convert Ax = b into x = Cx +d Generate a sequence of approximations (iteration) x 1 , x 2 , …., with initial x 0 Similar to fix-point iteration method Iterative Methods d Cx x b Ax + = = Equivalent system d Cx x 1 j j + = - f(x)=0 x=g(x) root finding
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Rearrange Matrix Equations Rewrite the matrix equation in the same way = + + + = + + + = + + + = + + + 4 4 44 3 43 2 42 1
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Lecture 24 - Chapter 11 Iterative Methods for System of...

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