The long-term dynamics of many dynamical systems evolves on a low-dimensional, attracting, invariant slow manifold, which can be parameterized by only a few variables (“observables”). The explicit derivation of such a slow manifold (and thus, the reduction of the long-term system dynamics) can be extremely difficult, or practically impossible. For this class of problems, the equation-free compu...

This document proposes a Newton step graph-based model for Quadratic separable Problems (QSP). The Newton step is well suited for this kind of problems, but when the problem size grows the matrix-based QSP model will grow in a non linear manner. Furthermore, handling the constraints becomes the main problem as we have to select the right constraints in the different solution steps. When this ha...

We prove the theoretical convergence of a short-step, approximate pathfollowing, interior-point primal-dual algorithm for semidefinite programs based on the Gauss-Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss-Newton direction in this context. It assumes strict complementarity and uniqueness of the ...

II More Experiments We present more experimental results that are not included in the main paper in this section. We consider the same experiment environment, and the same problem being solved. We present the results using different values of C to see the relative efficiency when the problems become more difficult or easier. The result of C = 10−3 is shown in Figure (I), and the result of C = 1...

In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and f -representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish ...

We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of ...

This paper discusses the usage of a two-dimensional electrochemical battery model of a lead acid battery cell as a state-of-health indicator in an embedded application. The model equations are a set of coupled highly non-linear partial differential equations that evolve with time. At each time step, these equations are solved using Newton’s Method, and a direct skyline LU solver without partial...

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes’ transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by ...

In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for p...

Periodic solutions of certain large scale systems of ODEs can be computed eeciently using a hybrid Newton-Picard scheme, especially in a continuation context. In this paper we describe and analyse a numerical method to accurately compute period doubling bifurcation points using the Newton-Picard approach. The method avoids the computation of the full monodromy matrix, which is present in the de...