Related papers: A Parareal Algorithm with Spectral Coarse Solver
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
We study forecasting capabilities of the methods of Singular Spectrum Analysis (SSA) and Local Approximation (LA). A practical implementation of these methods to several time series is described. Details of the algorithms of these methods…
We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows…
In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming (SDP) solvers is up to…
A variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse…
In this paper, we propose, analyze and implement efficient time parallel methods for the Cahn-Hilliard (CH) equation. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of…
Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
Parametric search has been widely used in geometric algorithms. Cole's improvement provides a way of saving a logarithmic factor in the running time over what is achievable using the standard method. Unfortunately, this improvement comes at…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the…
In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…