Related papers: Efficient Computation of Higher-Order Variational …
The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable…
Reactive trajectory optimization for robotics presents formidable challenges, demanding the rapid generation of purposeful robot motion in complex and swiftly changing dynamic environments. While much existing research predominantly…
In this paper, we present a variational integrator that is based on an approximation of the Euler--Lagrange boundary-value problem via Taylor's method. This can viewed as a special case of the shooting-based variational integrator. The…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…
The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schr\"{o}dinger equations. When applied to the nonlinear Gross-Pitaevskii equation, the method remains…
Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits…
This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives. Instead of computing full derivatives, which could be…
Numerical integration (NI) packages commonly used in scientific research are limited to returning the value of a definite integral at the upper integration limit, also commonly referred to as numerical quadrature. These quadrature…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is $C^1$ in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
Due to its reduced memory and computational demands, dynamical low-rank approximation (DLRA) has sparked significant interest in multiple research communities. A central challenge in DLRA is the development of time integrators that are…