|Title||A recursive algorithm for inversion of linear operator pencils|
|Presenter||Elizabeth Bradford (University of South Australia)|
|Author(s)||Amie Albrecht, Elizabeth Bradford, Phil Howlett and Geetika Verma|
|Session||Operations Research and Optimisation|
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.
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