In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and weakly perturbed cases, numerical integration is necessary in situations where the perturbation is relatively strong. Kustaanheimo{Stiefel (KS) regularizati...

We consider the unconstrained minimization of a continuously diierentiable function with semismooth gradient by line search methods; in particular we focus on the problem of the acceptance of the unit stepsize. We show that, under mild conditions, if the full search direction brings superlinear convergence, then the unit stepsize is eventually accepted so that the Maratos eeect does not occur. ...

This paper focuses on two types of artifacts—local variables and comments in a method (function). Both of them are usually used at the programer’s discretion. Thus, naming local variables and commenting code can vary among individuals, and such an individual difference may cause a dispersion in quality. This paper conducts an empirical analysis on the fault-proneness of Java methods which are c...

In this paper, we investigate a distributed Nash equilibrium seeking problem for a timevarying multi-agent network consisting of two subnetworks. We propose a subgradientbased distributed algorithm to seek a Nash equilibrium of a zero-sum game, where the two subnetworks share the same sum objective function. We show that the proposed distributed algorithm with homogenous stepsize can achieve a ...

The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and analyzed. In the context of time-dependent nonlinear Schrödinger equations, asymptotical correctness of the local error estimators associated...

A fundamental classification problem of data mining and machine learning is that of minimizing a strongly convex, piecewise quadratic function on the n-dimensional real space Rn. We show finite termination of a Newton method to the unique global solution starting from any point in Rn. If the function is well conditioned, then no stepsize is required from the start, and if not, an Armijo stepsiz...

The DI methods for directly solving a system of a general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergence for the variable order and stepsize case. 1. INTRODUCTION Many problems in engineering and science can be formulated in terms of such a system. The general system of higher orde...

Consider the consensus problem of minimizing f(x) = ∑n i=1 fi(x) where each fi is only known to one individual agent i belonging to a connected network of n agents. All the agents shall collaboratively solve this problem and obtain the solution via data exchanges only between neighboring agents. Such algorithms avoid the need of a fusion center, offer better network load balance, and improve da...

This paper presents adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method which departs from a wellunderstood selfadjoint problem. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contrib...