Two-frequency decomposition

Summary. 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 18] 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 . Numerical experiments demonstrate similar convergence behaviour for a wider class of problems.Mathematics Subject Classification (2000): 65F10, 65N22