Unformatted text preview: fastest iterative method, conjugate gradients with an incomplete Cholesky preconditioner, took 0.9 seconds. My implementation of multigrid for this problem took 4 iterations and 8.2 seconds. The virtue of multigrid, though, is if we want a Fner grid, we will probably still get convergence in about 4 iterations, while the number of iterations of the other algorithms increases with h , so eventually multigrid will win. CHALLENGE 32.4. The number of iterations remained 4 for κ = 10, 100, and − 10, but for κ = − 100, multigrid failed to converge. As noted in the challenge, a more complicated algorithm is necessary. Note that the function smooth.m is a much faster implementation of Gauss– Seidel than that given in the solution to Challenge 28.6 in Chapter 28....
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 Fall '11
 Dr.Robin
 Numerical Analysis, Multigrid, ﬁnest grid

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