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Unformatted text preview: Iterative Methods for Large Linear Systems Section 11.5 Not in Custom Edition use these slides Suppose that linear system Ax = b has 1 million equations and unknowns Gaussian elimination requires O(n 3 ) arithmetic operations 10 18 work is prohibitive Iterative methods for solving Ax=b can be more economical But they require and infinite number of iterations to give an exact solution Thus we terminate them when desired accuracy is reached Need an initial estimate of the solution General Iterative Method Idea: suppose that an estimate x of the solution is known. Compute the new estimate x 1 as: In general: A=L+D+U Strictly lower triangular diagonal strictly upper triangular Jacobis method Jacobis method Choose the matrix splitting as: Lower, diagonal, upper scalar form A= L+D+U Matrix form Jacobi Process one equation at a time: i=1,n Diagonal must be nonzero How fast does it converge? How fast does it converge?...
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 Fall '11
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 Economics

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