Solving piecewise linear systems in abs-normal form

Solving piecewise linear equations in abs-normal form

With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. As shown in [Gri13] PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL functions are obtained quite...

Piecewise Constant Controlled Linear Fuzzy Systems

Large-amplitude non-linear normal modes of piecewise linear systems

A numerical method for constructing non-linear normal modes (NNMs) for piecewise linear autonomous systems is presented. These NNMs are based on the concept of invariant manifolds, and are obtained using a Galerkin-based solution of the invariant manifold’s non-linear partial differential equations. The accuracy of the constructed non-linear modes is checked by the comparison of the motion on t...

The implications of piecewise linear process of normal accruals

The present study investigates whether the basic assumption in the Jones model, which normal accruals are a linear function of change in sales, is empirically valid. It also discusses and addresses the implications of the assumption violation in the earnings management detection tests. The research employs a sample of 2832 observations of the annual information of firms listed in Tehran Stock E...

Closed Form Periodic Solutions for Piecewise-linear Vibrating Systems

Piecewise-linear oscillators are often considered as finite degrees-of-freedom models of cracked elastic structures [1-3] but may also represent specifics of original systems. In many cases, the corresponding periodic solutions combine different pieces of linear solutions valid for two different subspaces of the configuration space [4,5]. It is always preferable though to deal with closed form ...