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Numerical experiments in Section 6 compare the bisection method with two other methods for Hermitian order one quasiseparable matrices: implicit QR after a reduction to tridiagonal form and divide and conquer.
In order to apply the bisection method just described, we a priori need a lower and an upper bound for the eigenvalues.
Sturm property with bisection for eigenvalues of Hermitian quasiseparable matrices.
The important rudiments for this method, Sturm property with bisection, appeared first in 1962 in [13].
6) is computed, all the other operations required to find v([lambda]) are the same and so is the small number of remaining operations needed to manage the bisection step itself.
3) contain a number of operations which do not involve the value [lambda], so that these operations can be executed in advance, such that in practice less operations are required for each bisection.
Since it is needed for each of the many bisection steps for each eigenvalue, we have to repeatedly evaluate the sequence in (3.
In total, the complexity of one bisection step in the present theorem is
10) requires one multiplication less for the semiseparable case, and this is why the bisection algorithm works 10% faster than for quasiseparable matrices.