Convergence results for some piecewise linear solvers

2020/12/04 by Radons, Manuel, Rump, Siegfried M.
#15A39 #90C27 #90C33 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2012.02520

Abstract

Let A be a real n× n matrix and z,b∈ \mathbb Rⁿ. The piecewise linear equation system z-A\vert z\vert = b is called an absolute value equation. We consider two solvers for this problem, one direct, one semi-iterative, and extend their previously known ranges of convergence.

Related

• Convergence results for some piecewise linear solvers
• Sign controlled solvers for the absolute value equation with an application to support vector machines
• On the convergence of iterative schemes for solving a piecewise linear system of equations
• On the semigroup property for some structured iterations
• Numerical solution of a class of quasi-linear matrix equations