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Fast solvers and Sylvester equations: both sides now

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1 Author(s)

We're using the structure of a problem with n2 unknowns to reduce the amount of computation from O(n6) (using the Cholesky decomposition) to O(n4) (exploiting sparsity) and then to O(n3) (using the Sylvester structure), a substantial savings when n is large. But knowing just a bit more about the problem's structure allows further reduction, down to O(n2 log2n) when n is a power of two. Because we're computing n2 answers, this is close to optimal, and it illustrates the value of exploiting every possible bit of structure in our problems.

Published in:

Computing in Science & Engineering  (Volume:7 ,  Issue: 6 )