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{\large Eran Treister \\
{\bf On Multiplicative and Additive Multigrid Schemes for Sparse Eigenproblems}}

Computer Science Department \\ Technion \\ Haifa 32000 \\ Israel
\\
{\tt eran@cs.technion.ac.il}\\
Irad Yavneh\end{center}

Multiplicative multigrid algorithms have recently been shown to be
powerful and robust, mainly as pure eigen-solvers or as a setup phase for
adaptive linear system solvers. However, such multiplicative algorithms
have one significant drawback, in that
they require recalculating the whole multigrid hierarchy of operators in
each cycle, entailing a relatively high computational cost. This work
suggests a scheme where multiplicative
and additive algorithms are applied in a complementary manner, with the
multiplicative solver providing the coarse-grid hierarchy to the additive
algorithm, and getting in return an improved solution with which to
construct better operators. This approach is demonstrated with two new
and improved versions of the recent adaptive Smoothed Aggregation
multiplicative method for solving Markov Chains.


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