Splittings for iterative solution of linear systems

Marko Huhtanen
Institute of Mathematics, Helsinki University of Technology
Box 1100, FIN-02015, Finland
marko.huhtanen@tkk.fi
Mikko Byckling

Consider iteratively solving a linear system $ Ax=b$, with invertible $ A\in \mathbb{C}^{n \times n}$ and $ b\in \mathbb{C}^n$, by splitting the matrix $ A$ as $ A=L+R$, where $ L$ and $ R$ are both readily invertible. In such a case the recently introduced residual minimizing Krylov subspace method [1] can be executed, allowing, in a certain sense, preconditioning simultaneously with $ L$ and $ R$.

Splittings satisfying $ A=L+R$ result either form the structure of the problem, or are algebraic. Splittings of Gauss-Seidel type belong to the latter category. In this talk we discuss such splittings of $ A$.

[1] M. Huhtanen and O. Nevanlinna, A minimum residual algorithm for solving linear systems, submitted manuscript available at www.math.hut.fi/~mhuhtane/index.html.