منابع مشابه
Absolute Value Equations
We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax − |x| = b, where A is an arbitrary n × n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give no...
متن کاملParticle Swarm Optimization for Absolute Value Equations
We investigate the NP-hard absolute value equation (AVE) Au |u| = b, where A is an arbitrary square matrix. In this paper, we present a smoothing method for the AVE. First, we replace the absolute value function by a smooth one, called aggregate function. With this smoothing technique, we formulate the non-smooth AVE as a smooth nonlinear equations, furthermore, an unconstrained differentiable ...
متن کاملA new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations
In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...
متن کاملAn improved generalized Newton method for absolute value equations
In this paper, we suggest and analyze an improved generalized Newton method for solving the NP-hard absolute value equations [Formula: see text] when the singular values of A exceed 1. We show that the global and local quadratic convergence of the proposed method. Numerical experiments show the efficiency of the method and the high accuracy of calculation.
متن کاملTwo Cscs-based Iteration Methods for Solving Absolute Value Equations∗
Recently, two families of HSS-based iteration methods are constructed for solving the system of absolute value equations (AVEs), which is a class of non-differentiable NP-hard problems. In this study, we establish the Picard-CSCS iteration method and the nonlinear CSCS-like iteration method for AVEs involving the Toeplitz matrix. Then, we analyze the convergence of the Picard-CSCS iteration met...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.05.004