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Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…

Numerical Analysis · Mathematics 2026-02-05 Erin Claire Carson

We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…

Numerical Analysis · Mathematics 2020-05-18 Niall Bootland , Alistair Bentley , Christopher Kees , Andrew Wathen

In this paper, we consider a class of difference-of-convex (DC) optimization problems, which require only a weaker restricted $L$-smooth adaptable property on the smooth part of the objective function, instead of the standard global…

Optimization and Control · Mathematics 2025-04-30 Lei Yang , Jingjing Hu , Kim-Chuan Toh

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

Numerical Analysis · Mathematics 2023-10-26 Fatemeh P. A. Beik , Michele Benzi

This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…

Optimization and Control · Mathematics 2023-11-15 Leon Eifler , Jules Nicolas-Thouvenin , Ambros Gleixner

Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate…

Optimization and Control · Mathematics 2018-01-04 Yangyang Xu

GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…

Computational Physics · Physics 2011-11-02 Yong-Chull Jang , Hyung-Jin Kim , Weonjong Lee

Extremely large-scale multiple-input-multipleoutput (XL-MIMO) has been reviewed as a promising technology for future sixth-generation (6G) networks to achieve higher performance. In practice, various linear precoding schemes, such as…

Information Theory · Computer Science 2023-05-24 Bokai Xu , Jiayi Zhang , Jiaxun Li , Huahua Xiao , Bo Ai

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…

Computational Physics · Physics 2011-08-24 Eiji Tsuchida , Yoong-Kee Choe

This paper presents a novel accelerated distributed algorithm for unconstrained consensus optimization over static undirected networks. The proposed algorithm combines the benefits of acceleration from momentum, the robustness of the…

Optimization and Control · Mathematics 2024-05-15 Eduardo Sebastián , Mauro Franceschelli , Andrea Gasparri , Eduardo Montijano , Carlos Sagüés

Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…

Software Engineering · Computer Science 2022-03-16 Dorra Ben Khalifa , Matthieu Martel

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…

Optimization and Control · Mathematics 2021-01-06 Xiang Li , Zhihua Zhang

The implementation of the conjugate gradient (CG) method for massive MIMO detection is computationally challenging, especially for a large number of users and correlated channels. In this paper, we propose a low computational complexity CG…

Signal Processing · Electrical Eng. & Systems 2026-04-28 Yiming Fang , Li Chen , Changsheng You , Dingzhu Wen , Pengcheng Zhu

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

Optimization and Control · Mathematics 2025-12-12 Chenglong Bao , Yancheng Yuan , Shulan Zhu

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

Optimization and Control · Mathematics 2011-09-14 Q. Tran Dinh , C. Savorgnan , M. Diehl

We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…

Numerical Analysis · Mathematics 2026-04-01 Youssef Diouane , Selime Gürol , Oussama Mouhtal , Dominique Orban

We deal with accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). The sequence originates from time-stepping within a simulation of an unsteady incompressible flow. We…

Numerical Analysis · Mathematics 2026-02-04 Martin Hanek , Jan Papež , Jakub Šístek

In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical…

Numerical Analysis · Mathematics 2019-05-07 M. Bauer , M. Bebendorf

Reducing memory traffic is critical to accelerate Lattice QCD computations on modern processors, given that such computations are memory-bandwidth bound. A commonly used strategy is mixed-precision solvers, however, these require careful…

High Energy Physics - Lattice · Physics 2023-02-21 M. A. Clark , Dean Howarth , Jiqun Tu , Mathias Wagner , Evan Weinberg

This paper presents a hierarchical low-rank decomposition algorithm assuming any matrix element can be computed in $O(1)$ time. The proposed algorithm computes rank-revealing decompositions of sub-matrices with a blocked adaptive cross…

Numerical Analysis · Mathematics 2019-09-06 Yang Liu , Wissam Sid-Lakhdar , Elizaveta Rebrova , Pieter Ghysels , Xiaoye Sherry Li