相关论文: Alternating Anderson-Richardson method: An efficie…

Searching for potential active compounds in large databases is a necessary step to reduce time and costs in modern drug discovery pipelines. Such virtual screening methods seek to provide predictions that allow the search space to be…

A new algorithm called accelerated projection-based consensus (APC) has recently emerged as a promising approach to solve large-scale systems of linear equations in a distributed fashion. The algorithm adopts the federated architecture, and…

Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…

We present a parallelizable SSOR preconditioning scheme for Krylov subspace iterative solvers which proves to be efficient in lattice QCD applications involving Wilson fermions. Our preconditioner is based on a locally lexicographic…

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of…

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…

Handling contaminated data poses a critical challenge in anomaly detection, as traditional models assume training on purely normal data. Conventional methods mitigate contamination by relying on fixed contamination ratios, but discrepancies…

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…

Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…

The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…

Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…

In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice…

Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a…

Robust and efficient solvers for coupled-adjoint linear systems are crucial to successful aerostructural optimization. Monolithic and partitioned strategies can be applied. The monolithic approach is expected to offer better robustness and…

In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm for scalar functions. It builds on the set-valued AAA…

The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…

Alternating least squares (ALS) is often considered the workhorse algorithm for computing the rank-R canonical tensor approximation, but for certain problems its convergence can be very slow. The nonlinear conjugate gradient (NCG) method…

Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…

We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…