In this talk we consider the inheritance of different types of spectral equivalence in algebraic multilevel methods.
In detail we obtain a two level preconditioner
Here and
are approximations of
and
respectively.
In the talk we assume that and
have some spectral property
related to
and
respectively and show
that
defined by (
) has the same property related
to
.
This leads also to new condition number bounds for two level methods applied as preconditioner.
These can be used to obtain new bounds for the multilevel preconditioner and the so called AMLI preconditioner
At the end of the talk we will see that for specific C.B.S. constants the new bounds improve well-known bounds.