This article considers the design and implementation of variable-timestep methods for simulating holonomically constrained mechanical systems. Symplectic variable stepsizes are briefly discussed, we then consider time-reparameterization techniques employing a time-reversible (symmetric) integration method to solve the equations of motion. We give several numerical examples, including a simulati...

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form min{φ(Bu)+ 1/2‖Au− f ‖2}, where φ may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstructio...

In this article, block BS methods are considered for the numerical solution of Volterra integro-differential equations (VIDEs). Convergence and stability properties are analyzed. A new Matlab code for the solution of VIDEs, called VIDEBS, is presented. Numerical results using a variable stepsize implementation show the effectiveness of the proposed code. 2014 Elsevier Inc. All rights reserved.

We describe an extension of the Taylor method for numerical solution ODEs that uses Padé approximants to obtain extremely precise results. The accuracy results is essentially limited only by computer time and memory, provided one works in arbitrary precision. In this stepsize adjusted achieve desired (variable stepsize), while order expansion can be either fixed or changed at each iteration ord...

We propose a diagonal metric selection for variable metric proximal gradient method (VMPG). The proposed metric better captures the local geometry of the problem and provides improved convergence compared to the standard proximal gradient (PG) methods with Barzilai-Borwein (BB) stepsize selection. Further, we provide convergence guarantees for the proposed method and illustrate its advantages o...