异步算法的收敛性结果及其应用

Asynchronous parareal time discretization for partial differential equations

Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks, this paper advocates a novel application direction targeting time-decomposed time-parallel approaches. Specifically, an asynchronous iterative model is derived from the Parareal scheme, for which convergence and speedup analysis are then conducted. It turned out that Parareal and async-Parareal feature very close convergence conditions, asymptotically equivalen…

An Asynchronous Parallel Randomized Kaczmarz Algorithm

We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of processors is bounded by a multiple of the number of rows in $A$.

An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids

We present a study of the effectiveness of asynchronous incomplete LU factorization preconditioners for the time-implicit solution of compressible flow problems while exploiting thread-parallelism within a compute node. A block variant of the asynchronous fine-grain parallel preconditioner adapted to a finite volume discretization of the compressible Navier-Stokes equations on unstructured grids is presented, and convergence theory is extended to the new variant. Experimental (numerical) results on the performance of these preconditioners on inviscid and viscous laminar two-dimensional steady-…

M矩阵上步异步超松弛法的上范数收敛性

Supremum-Norm Convergence for Step-Asynchronous Successive Overrelaxation on M-matrices

研究步异步超松弛法在M矩阵上的收敛性，证明其能以几何速率减小误差的w-范数，并展示如何通过选择合适的w向量来估计绝对误差的上界。

Asynchronous global-local non-invasive coupling for linear elliptic problems

This paper presents the first asynchronous version of the Global/Local non-invasive coupling, capable of dealing efficiently with multiple, possibly adjacent, patches. We give a new interpretation of the coupling in terms of primal domain decomposition method, and we prove the convergence of the relaxed asynchronous iteration. The asynchronous paradigm lifts many bottlenecks of the Global/Local coupling performance. We illustrate the method on several linear elliptic problems as encountered in thermal and elasticity studies.

异步坐标下降法在更现实假设下的应用

Asynchronous Coordinate Descent under More Realistic Assumptions

本文在更现实的假设下证明了异步并行块坐标下降法的收敛性，不依赖独立性假设，适用于有界和无界延迟，覆盖非凸、弱凸和强凸函数。

关于异步并行迭代与无界延迟收敛性分析

On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

本文从概率角度分析了异步并行方法在无界延迟下的收敛性，给出了依赖延迟统计的显式步长公式，并通过实验验证了理论模型的正确性，展示了传统最大延迟诱导步长过于保守的问题。

Asynchronous Time-Parallel Method based on Laplace Transform

Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor, which leads to a lot of wasted time. In this paper, we propose an original asynchronous Laplace transform method formalized for quasilinear problems based on the well-known Gaver-Stehfest algorithm. Parallel experiments show the convergence of our new method, as well as several interesting properties compared with the classical algorithms.

非凸优化中的异步并行随机梯度

Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization

本文研究了非凸优化中两种异步并行随机梯度方法，证明了其在计算机网络和共享内存系统中的渐进收敛率，并展示了线性加速的可能性。

更多每秒迭代次数，相同质量——为什么异步算法可能大幅超越传统算法

More Iterations per Second, Same Quality -- Why Asynchronous Algorithms may Drastically Outperform Traditional Ones

本文研究了异步并行算法ARock的收敛性，证明在大规模问题中，异步算法所需的额外迭代次数可忽略，从而证明其在分布式计算中的潜力。