Related papers: Solving Linear Equations Using a Jacobi Based Time…
A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…
We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…
We propose and analyze a Vanka-type multigrid solver for solving a sequence of complex-shifted Laplacian systems arising in diagonalization-based parallel-in-time algorithms for evolutionary equations. Under suitable assumption, local…
The possibility to use competitive evolutionary algorithms to generate long-term progress is normally prevented by the convergence on limit cycle dynamics in which the evolving agents keep progressing against their current competitors by…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
The Jacobi evolution method has been widely used in the QCD analysis of structure function data. However a recent paper claims that there are serious problems with its convergence and stability. Here we briefly review the evidence for the…
The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…
A novel population-based heuristic algorithm called the adaptive and various learning-based algorithm (AVLA) is proposed for solving general optimization problems in this paper. The main idea of AVLA is inspired by the learning behaviors of…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
We propose fork-join and task-based hybrid implementations of four classical linear algebra iterative methods (Jacobi, Gauss-Seidel, conjugate gradient and biconjugate gradient stabilised) as well as variations of them. Algorithms are duly…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
We introduce a new machinery to study the large time behavior for general classes of Hamilton--Jacobi type equations, which include degenerate parabolic equations and weakly coupled systems. We establish the convergence results by using the…
We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in a previous paper…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an…
As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the…