Related papers: Convergence analysis of a parareal algorithm with …
A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is…
A major challenge in current optimization research for deep learning is to automatically find optimal step sizes for each update step. The optimal step size is closely related to the shape of the loss in the update step direction. However,…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…
Given the image collection of an object, we aim at building a real-time image-based pose estimation method, which requires neither its CAD model nor hours of object-specific training. Recent NeRF-based methods provide a promising solution…
We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the…
We show that the forward and backward propagation can be formulated as a solution of lower and upper triangular systems of equations. For standard feedforward (FNNs) and recurrent neural networks (RNNs) the triangular systems are always…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm…
We investigate the integration of Nesterov-type acceleration into primal-dual methods for structured convex optimization. While proximal splitting algorithms efficiently handle composite problems of the form $\min_x f(x)+g(x)+h(Kx)$,…
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…
This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
Variable steps implicit-explicit multistep methods for PDEs have been presented in [17], where the zero-stability is studied for ODEs; however, the stability analysis still remains an open question for PDEs. Based on the idea of linear…
This paper considers the problem of distributed estimation in an incremental network when the measurements taken by the node follow a widely linear model. The proposed algorithm which we refer to it as incremental augmented affine…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…