Overview It has long been known that the solutions produced by adaptive solvers for ordinary differential (ODE) and differential algebraic (DAE) systems, while generally reliable, are not smooth with respect to perturbations in initial conditions or other problem parameters. Söderlind and Wang [12, 13] have recently developed a digital filter stepsize controller that has a theoretical basis fro...

The existing distributed algorithms for Network Utility Maximization (NUM) problems are mostly constructed using dual decomposition and first-order (gradient or subgradient) methods, which suffer from slow rate of convergence. Recent work [25] proposed an alternative distributed Newton-type algorithm for solving NUM problems with self-concordant utility functions. For each primal iteration, thi...

In this letter, we address the distributed optimization problem with event-triggered communication by notion of input feedforward passivity (IFP). First, analyze continuous-time algorithm over uniformly jointly strongly connected balanced digraphs in an IFP-based framework. Then, propose a mechanism for algorithm. Next, discretize forward Euler method constant stepsize irrelevant to network siz...

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we call delay, is the number of times it has been updated since its creation. Almos...

When numerically tracking implicitly-defined paths, such as is required for homotopy continuation methods, efficiency and reliability are enhanced by using adaptive stepsize and adaptive multiprecision methods. Both efficiency and reliability can be further improved by adapting precision and stepsize simultaneously. This paper presents a strategy for adjusting precision and stepsize together to...

Online Newton step algorithms usually achieve good performance with less training samples than first order methods, but require higher space and time complexity in each iteration. In this paper, we develop a new sketching strategy called regularized frequent direction (RFD) to improve the performance of online Newton algorithms. Unlike the standard frequent direction (FD) which only maintains a...

Developing new and efficient numerical integration techniques is of great importance in applied mathematics computer science. Among the variety available methods, multistep ODE solvers are broadly used simulation software. Recently, semi-implicit proved to be an compromise between implicit explicit solvers, multiple high-performance methods were proposed. However, computational efficiency any s...

This report is devoted to the study and to the comparison of methods for estimation of the local error and for adaptive step-size control when solving the generalised nonlinear Schrodinger equation (GNLSE) in optics by the Interaction Picture (IP) method or by the Symmetric Split-Step (S3F) method. Namely, we propose and study the use of an embedded Runge-Kutta method to solve the nonlinear pro...

Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators desirable their stability properties, significantly relaxing restrictions on timestep size. However, implicit require solutions to one or more systems nonlinear equations at each timestep, which large simulations can be prohibitively ex...