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{\large Karsten Kahl \\
{\bf Bootstrap Algebraic Multigrid}}

%% Gau�stra�e 20 \\ 42119 Wuppertal \\ Germany
Gau{\ss}stra{\ss}e 20 \\ 42119 Wuppertal \\ Germany
\\
{\tt kkahl@math.uni-wuppertal.de}\\
Achi Brandt\\
James Brannick\\
Karsten Kahl\\
Ira Livshits\end{center}

We develop an Algebraic Multigrid (AMG) cycling scheme based on the
adaptive Bootstrap AMG
framework. The approach we present adaptively computes a set of test vectors and then
uses them to define interpolation.

The setup of the method consists of two parts. First, we introduce concept of
Least Squares Interpolation which allows us to define interpolation in an algebraic
multigrid context that is solely based on a set of test vectors. In addition, we propose
and analyze a Bootstrap process to enhance the set of test vectors used in the
definition of Least Squares Interpolation in a multigrid fashion. We demonstrate
that this setup procedure allows us to iteratively improve the multigrid hierarchy
until suitable performance of the resulting method is achieved while
retaining control over
the complexity of the multigrid hierarchy and overall setup costs. We present tests for
a variety of applications that show the flexibility and robustness of this approach.


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