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Tests on the symmetric eigenvalue solver

In this section several numerical tests are performed to compare the traditional algorithm for finding all the eigenvalues with the new semiseparable approach. The algorithm is based on the $ QR$-step as described in Section 9.2 and Section 9.4, and implemented in a recursive way: if division in blocks is possible (i.e., that the deflation criterion is satisfied) because of the convergence behavior, then these blocks are dealt with separately.

Before starting the numerical tests some remarks have to be made: first of all the complexity of the reduction of a symmetric matrix into a similar semiseparable one costs $ 9 n^2 + O(n)$ flops more than the reduction of a matrix to tridiagonal form. An implicit $ QR$-step applied to a symmetric tridiagonal matrix costs $ 31 n$ flops while it costs $ \approx 10n$ flops more for a symmetric semiseparable matrix. However, this increased complexity is compensated when comparing the number of iteration steps the traditional algorithm needs with the number of steps the semiseparable algorithm needs. Figures about these results can be found in the following tests.



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next up previous contents index
Next: The block experiment Up: Implementations and numerical experiments Previous: The implementation of the   Contents   Index
Raf Vandebril 2004-05-03