Two-frequency decomposition

In this paper, we present a preconditioner for large systems of linear equations based on the block decomposition for block-tridiagonal matrices. This decomposition is in many respects similar to the frequency-filtering method of Wittum [8] and also to the frequency-filtering decomposition of Wagner [4]-[6]. In contrast to these methods, our approach requires no pointwise filtering conditions but, as in [1], only averaged ones; this simplifies the implementation without any loss of efficiency. Theoretical analysis of the model problem leads to the convergence rate 1 - O(h^1/3). Numerical experiments demonstrate similar convergence behaviour for a wider class of problems.