Abstract
In this paper, we present the tangential block decomposition for block-tridiagonal matrices which is in many aspects similar to the frequency filtering method by Wittum [8] and also to the tangential frequency filtering decomposition by Wagner [6]–[7]. In opposite to the methods of Wittum and Wagner, for the class of model problems our approach does not use any test vectors for its implementation. Similar to many iterative methods, it needs only bounds for extremal eigenvalues. Theoretical properties of our scheme are similar to those for the ADI-method. The practical convergence of the presented method is illustrated by numerical examples.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Axelson, O., Polman, B.: A robust preconditioner based on algebraic substructuring and two-level grids. In: Robust multigrid methods (Hackbusch, W., ed.), pp. 1–26. NNFM Bd. 23. Braunschweig: Vieweg-Verlag 1989.
Hackbusch, W.: Iterative solution of large sparse systems of equations. New York: Springer 1993.
Kettler, R.: Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods. In: Multigrid methods, Proceedings, Köln-Porz, 1981 (Hackbusch, W., Trottenberg, V., eds.), pp. 502–534. Berlin Heidelberg, New York Tokyo: Springer.
Samarskij, A. A., Nikolaev, E. S.: Numerical methods for grid equations. Vol. 2: Iterative methods. Basel: Birkhäuser 1989.
Varga, R.: Matrix iterative analysis. Englewood Cliffs: Prentice-Hall 1962.
Wagner, C.: Frequenzfilternde Zerlegungen für unsymmetrische Matrizen und Matrizen mit stark variierenden Koeffizienten. PhD Thesis, University of Stuttgart, 1995.
Wagner, C.: Tangential frequency filtering decompositions for symmetric matrices. Numer. Math.78, 143–163 (1997).
Wittum, G.: Filternde Zerlegungen—Schnelle Löser für große Gleichungssysteme. Teubner Skripten zur Numerik, Band 1, Stuttgart: Teubner 1992.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Buzdin, A. Tangential decomposition. Computing 61, 257–276 (1998). https://doi.org/10.1007/BF02684353
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02684353