sparse systems
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An improved affine projection sign algorithm (APSA) was developed herein using a ℒp-norm-like constraint to increase the convergence rate in sparse systems. The proposed APSA is robust against impulsive noise because APSA-type algorithms are generally based on the ℒ1-norm minimization of error signals. Moreover, the proposed algorithm can enhance the filter performance in terms of the convergence rate due to the implementation of the ℒp-norm-like constraint in sparse systems. Since a novel cost function of the proposed APSA was designed for maintaining the similar form of the original APSA, these have symmetric properties. According to the simulation results, the proposed APSA effectively enhances the filter performance in terms of the convergence rate of sparse system identification in the presence of impulsive noises compared to that achieved using the existing APSA-type algorithms.

In this paper are analyzed behavior and properties for different Krylov methods applied in different categories of problems. These categories often include PDEs, econometrics and network models, which are represented by large sparse systems. For our empirical analysis are taken into consideration size, the density of non-zero elements, symmetry/un-symmetry, eigenvalue distribution, also well/ill-conditioned and random systems. Convergence, approximation error and residuals are compared for the full version of methods, some restarted methods and preconditioned methods. Two preconditioners are considered respectively, ILU(0) and IC(0) by using at least five preconditioning techniques. In each case, empirical results show which technique is best to use based on properties of the system and are backed up by general theoretical information already found on Krylov space methods.

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Krylov subspace methods that relies on a modern inverse-based multilevel ILU (incomplete LU) preconditioning technique.We present new data-parallel versions of the preconditioner and the most important solvers contained in the package that significantly improve its performance without affecting its accuracy. Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration. The results obtained show a sensible reduction in the runtime of the methods, as well as the possibility of addressing large-scale problems efficiently.