Related papers: Order reductions of Lorentz-Dirac-like equations
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…
Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with…
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal…
In this paper we deal with a first order evolution inclusion involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a double step time-semidiscrete approximation,…
Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
In this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate subsequences (x_{g_n}) for every linear recurrent sequence…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative…
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
We present a novel way of constructing reduced models for systems of ordinary differential equations. The reduced models we construct depend on coefficients which measure the importance of the different terms appearing in the model and need…
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…
The classical Lorenz lowest order system of three nonlinear ordinary differential equations, capable of producing chaotic solutions, has been generalized by various authors in two main directions: (i) for number of equations larger than…
The behaviour of solutions to fourth order problems is studied through the decomposition into a system of second order ones, which leads to relaxed formulations with the introduction of measure terms. This allows to solve a shape…
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…