@phdthesis{Tichy2011, author = {Tichy, Michael}, title = {On algebraic aggregation methods in additive preconditioning}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-56541}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2011}, abstract = {In the following dissertation we consider three preconditioners of algebraic multigrid type, though they are defined for arbitrary prolongation and restriction operators, we consider them in more detail for the aggregation method. The strengthened Cauchy-Schwarz inequality and the resulting angle between the spaces will be our main interests. In this context we will introduce some modifications. For the problem of the one-dimensional convection we obtain perfect theoretical results. Although this is not the case for more complex problems, the numerical results we present will show that the modifications are also useful in these situation. Additionally, we will consider a symmetric problem in the energy norm and present a simple rule for algebraic aggregation.}, subject = {Pr{\"a}konditionierung}, language = {en} }