Abstract
| There are numerous examples of systems that can be represented by linear
equations. In many cases the system coefficient is an operator that depends on
an unknown parameter. We are interested in what happens to the solution when we
change this parameter. If the coefficient is a linear operator pencil which
depends on a single complex parameter and the resolvent is analytic on a deleted
neighbourhood of the origin, we will show that the resolvent can be calculated
by a recursive reduction procedure. We calculate this resolvent matrix using
this recursive reduction procedure which, for finite dimensional problems, will
terminate after a finite number of steps. In the infinite case this is not
always possible. I will illustrate with an example. |