相关论文: Fast sixth-order algorithm based on the generalize…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
The generalized Gearhart-Koshy acceleration is a recent exact affine search technique designed for the method of cyclic projections onto hyperplanes, i.e., the Kaczmarz method. However, its convergence properties, particularly the linear…
Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface.…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
In this paper we present an algorithm for optical phase evaluation based on the wavelet transform technique. The main advantage of this method is that it requires only one fringe pattern. This algorithm is based on the use of a second…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…
In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of $u'(t)$ with the kernel $(t_n-t)^{-\alpha}$. In the fast algorithm, the…
The Kaczmarz method is a row-action method for solving consistent non-square linear systems, and Gearhart-Koshy acceleration is a line-search that minimizes the Euclidean norm of the error along a ray in the direction of a Kaczmarz step.…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results…
In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…