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##

The shift

The choice of the shift is very important to achieve a fast
convergence about one of the eigenvalues. The shifts we consider here are
discussed in [91]. More references towards analysis of
different shifts can also be found there. Suppose we have the
following semiseparable matrix represented with the Givens-vector
representation:

One can choose as a shift, the so-called Rayleigh shift, or one
can consider as a shift the eigenvalue of

that is closest to , the Wilkinson shift [190]. Using this shift
in the tridiagonal case will give cubic convergence. The numerical
results provided in Chapter 9 will experimentally prove the same
rate of convergence for the symmetric semiseparable case.

** Next:** An implicit -step on
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Raf Vandebril
2004-05-03