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Differential Equations Solutions 164

# Differential Equations Solutions 164 - double-precision...

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174 Chapter 28. Solutions: Iterative Methods for Linear Systems CHALLENGE 28.6. The solution to these five problems is given on the website in solution20.m . The results for the square domain are shown in Figures 28.1 and 28.2. Gauss-Seidel took too many iterations to be competitive. The parameter cut is the drop-tolerance for the incomplete Cholesky decomposition. The AMD- Cholesky decomposition was the fastest algorithm for this problem, but it required 5.4 times the storage of cg and 2.6 times the storage of the pcg algorithm with incomplete Cholesky preconditioner for the problem of size 16129. Without reorder- ing, Cholesky was slow and very demanding of storage, requiring almost 30 million
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Unformatted text preview: double-precision words For the largest problem (almost 70 times as much as For the AMD reordering). Gauss-Seidel took a large amount oF time per iteration. This is an artiFact oF the implementation, since it is a bit tricky to get MATLAB to avoid working with the zero elements when accessing a sparse matrix row-by-row. Challenge: look at the program in gauss seidel.m and try to speed it up. A better version is provided in the solution to Challenge 32.4. Results For the domain with the circle cut out were similar; see ±igures 28.3 and 28.4....
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