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Stationary iterative methods for solving systems of linear equations are considered by some as out of date and out of favor, as compared to methods based on Krylov subspace iterations. However, these methods are still useful in many circumstances because they are easier to implement and, more importantly, can be used as pre-conditioners in combination with Krylov-subspace methods. In this note,...

In the simulation of continuous events, such as the ow of a uid through a pipe, or the ow of air around an aircraft, one usually imposes a grid over the area of interest and one restricts oneself to the computation of relevant parameters, for instance the pressure or the velocity of the ow or the temperature, in the gridpoints. Physical laws lead to approximate relations between these parameter...

In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank methods, the proposed algorithm tracks the optimal point in the sense of minimizing the ‘true’ mean square error (MSE) in the Krylov subspace, even when the esti...

A unified view of several recently introduced reduced-rank adaptive filters is presented. As all considered methods use Krylov subspace for rank reduction, the approach taken in this work is inspired from Krylov subspace methods for iterative solutions of linear systems. The alternative interpretation so obtained is used to study the properties of each considered technique and to relate one red...

Systems AVRAM SIDI Computer Science Department Technion Israel Institute of Technology Haifa 32000 ISRAEL E-mail: [email protected] http://www.cs.technion.ac.il/ ̃asidi/ Abstract: We consider the solution by Krylov subspace methods of a certain class of hermitian indefinite linear systems, such as those that arise from discretization of the Stokes equations in incompressible fluid mechanic...