相关论文: A stable one-synchronization variant of reorthogon…

In this paper we present a novel algorithm developed for computing the QR factorisation of extremely ill-conditioned tall-and-skinny matrices on distributed memory systems. The algorithm is based on the communication-avoiding CholeskyQR2…

Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous…

On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of $s$-step Krylov subspace method variants, in which iterations are…

This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or…

We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine…

In this article, we study the numerical solution of the one dimensional nonlinear sine-Gordon by using the modified cubic B-spline differential quadrature method. The scheme is a combination of a modified cubic B spline basis function and…

Update order is one of the major design choices of block decomposition algorithms. There are at least two classes of deterministic update orders: nonsymmetric (e.g. cyclic order) and symmetric (e.g. Gaussian back substitution or symmetric…

We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…

We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze stability of the cluster synchronous solution. Our approach has several advantages…

Resource scheduling is critical in many industries, especially in power systems. The Unit Commitment problem determines the on/off status and output levels of generators under many constraints. Traditional exact methods, such as…

Offline reinforcement learning and offline inverse reinforcement learning aim to recover near-optimal value functions or reward models from a fixed batch of logged trajectories, yet current practice still struggles to enforce Bellman…

Existing block Kaczmarz methods face challenges in balancing computational efficiency and convergence for large sparse linear systems with scattered nonzero patterns, due to costly partitioning strategies and non-orthogonal projections. In…

We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to…

This paper describes an implementation of the L-BFGS method designed to deal with two adversarial situations. The first occurs in distributed computing environments where some of the computational nodes devoted to the evaluation of the…

Asynchronous federated learning mitigates the inefficiency of conventional synchronous aggregation by integrating updates as they arrive and adjusting their influence based on staleness. Due to asynchrony and data heterogeneity, learning…

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse…

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

In this paper, we propose a gradient-based block coordinate descent (BCD-G) framework to solve the joint approximate diagonalization of matrices defined on the product of the complex Stiefel manifold and the special linear group. Instead of…

This paper considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to minimize the aggregate cost function, while they exchange information only with…

We propose an algorithm, called OEM (a.k.a. orthogonalizing EM), intended for var- ious least squares problems. The first step, named active orthogonization, orthogonalizes an arbi- trary regression matrix by elaborately adding more rows.…