相关论文: A numerically stable communication-avoiding s-step…

It is well known that for singular inconsistent range-symmetric linear systems, the generalized minimal residual (GMRES) method determines a least squares solution without breakdown. The reached least squares solution may be or not be the…

In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…

When the CG method for solving linear algebraic systems was formulated about 70 years ago by Lanczos, Hestenes, and Stiefel, it was considered an iterative process possessing a mathematical finite termination property. CG was placed into a…

We perform a backward stability analysis of preconditioned sketched GMRES [Nakatsukasa and Tropp, SIAM J. Matrix Anal. Appl, 2024] for solving linear systems $Ax=b$, and show that the backward stability at iteration $i$ depends on the…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…

We present a stepping stabilization control that addresses external push disturbances on bipedal walking robots. The stepping control is synthesized based on the step-to-step (S2S) dynamics of the robot that is controlled to have an…

Training Graph Neural Networks (GNNs) on large graphs is challenging due to the conflict between the high memory demand and limited GPU memory. Recently, distributed full-graph GNN training has been widely adopted to tackle this problem.…

We propose a more realistic version of the recently introduced split-step model (SSM), which consists of periodically alternating dispersive and nonlinear segments, by adding uniformly distributed loss and lumped gain to it. In the case…

Self-stabilization is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is self-stabilizing if it is able to recover without external intervention from any catastrophic…

Distributed Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental operation in high-performance computing and deep learning applications. The major performance bottleneck in distributed SpMM lies in substantial communication overhead,…

Electromigration (EM) induced stress evolution is a major reliability challenge in nanometer-scale VLSI interconnects. Accurate EM analysis requires solving stress-governing partial differential equations over large interconnect trees,…

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS)…

In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools…

For simulating large networks of neurons Hines proposed a method which uses extensively the structure of the arising systems of ordinary differential equations in order to obtain an efficient implementation. The original method requires…

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…

Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…

We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these problems we prove that, under mild assumptions, gradient descent converges to their…

Distributed computing is a standard way to scale up machine learning and data science algorithms to process large amounts of data. In such settings, avoiding communication amongst machines is paramount for achieving high performance. Rather…

While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper…