We propose a hybrid algorithm for solving the NP-hard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving iteratively a linear system of equations followed by a linear program. The algorithm was tested on 100 consecutively generated random solvable instances of the AVE with n =50...

In this paper, we reformulate the NP-hard problem of the absolute value equation (AVE) as a horizontal linear complementarity one and then solve it using a smoothing technique. This approach leads to a new class of methods that are valid for general absolute value equation. An asymptotic analysis proves the convergence of our schemes and provides some interesting error estimates. This kind of e...

In traditional denoising techniques, filters and Short time Fourier transform are not so good for speech signal denoising. Wavelet thresholding de-noising techniques provide a new way to reduce background noise in speech signal. However, the soft thresholding is best in reducing noise but worst in preserving edges, and hard thresholding is best in preserving edges but worst in de-noising. In th...

The ability to map the spatial variation of the absolute, rather than the relative value of the equilibrium magnetization could be advantageous in many areas of NMR. However, direct measurement of M(0) is usually difficult because of the multiparametric dependence of the NMR signal. Here we propose a technique for mapping the spatial variation of the absolute value of M(0), independent of relax...

∗Received by the editors March 10, 2009. Accepted for publication August 27, 2009. Handling Editor: Daniel Szyld. †Institute of Computer Science, Czech Academy of Sciences, Prague, and School of Business Administration, Anglo-American University, Prague, Czech Republic ([email protected]). Supported by the Czech Republic Grant Agency under grants 201/09/1957 and 201/08/J020, and by the Institution...

We formulate the NP-hard absolute value equation as linear complementary problem when the singular values of A exceed one, and we proposed a mixed integer linear programming method to absolute value equation problem. The effectiveness of the method is demonstrated by its ability to solve random problems.

We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax− |x| = b, where A is an n× n square matrix. The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program. The...

It is proved that applying sufficient regularity conditions to the interval matrix [A − |B|, A + |B|], we can create a new unique solvability condition for the absolute value equation Ax + B|x| = b, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive definiteness of a certain point mat...

in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...

In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to understand why and when sparse filtering does work. We provide a thorough theoretical analysis of sparse filtering and its properties, and further offer an experiment...