


Abstract
Lars Grasedyck, Wed, 15.3016.00

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A Multigrid Method to Solve Large Scale Sylvester Equations
Lars Grasedyck (MPI Leipzig)
(joint work with Wolfgang Hackbusch)
The talk is subdivided into three parts.
In the first part we give a brief and incomplete
overview of the existing methods for the solution of
large scale matrix equations, namely Lyapunov,
Sylvester and Riccati equations.
In the second part the framework for multigrid methods
(geometric and algebraic) for Sylvester equations is
introduced. These allow to compute the N by N solution
matrix in O(N^{2}).
In the last part we consider a framework that
preserves a given lowrank structure in the righthand
side as it is naturally given in the context of model
reduction. For N by N matrices we can compute the
N by N solution matrix in O(N log^{2} N) complexity.
The talk closes with some numerical examples.




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