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Sparse linear system solvers ($Ax=b$) are critical computational kernels in Electronic Design Automation (EDA), underpinning vital simulations for modern IC and system design. Applications like power integrity verification and…

Numerical Analysis · Mathematics 2025-04-17 Nityanand Rai

Linear Programs (LPs) appear in a large number of applications and offloading them to the GPU is viable to gain performance. Existing work on offloading and solving an LP on GPU suggests that performance is gained from large sized LPs…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-09-27 Amit Gurung , Rajarshi Ray

This survey describes a class of methods known as "fast direct solvers". These algorithms address the problem of solving a system of linear equations $\boldsymbol{Ax}=\boldsymbol{b}$ arising from the discretization of either an elliptic PDE…

Numerical Analysis · Mathematics 2025-11-12 Per-Gunnar Martinsson , Michael O'Neil

Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…

Numerical Analysis · Mathematics 2025-12-23 Manuel Liebchen , Robert Jendersie , Utku Kaya , Christian Lessig , Thomas Richter

We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…

Optimization and Control · Mathematics 2026-03-03 Jiachang Liu , Andrea Lodi , Soroosh Shafiee

To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…

Computational Engineering, Finance, and Science · Computer Science 2021-04-29 Zhenqi Wang , Sebastian Wende-von Berg , Martin Braun

Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…

Numerical Analysis · Mathematics 2011-05-02 Anoosh Abdy

We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-09-29 Ang Li , Radu Serban , Dan Negrut

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…

Mathematical Software · Computer Science 2017-10-16 Ruipeng Li

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…

Optimization and Control · Mathematics 2021-11-29 Valentina De Simone , Daniela di Serafino , Jacek Gondzio , Spyridon Pougkakiotis , Marco Viola

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-02-13 M. Ozan Karsavuran , Esmond G. Ng , Barry W. Peyton

In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid…

Signal Processing · Electrical Eng. & Systems 2019-06-04 Cheng-Yu Hung , Mostafa Kaveh

Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…

Optimization and Control · Mathematics 2019-07-15 Juraj Kardoš , Drosos Kourounis , Olaf Schenk

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…

Computer Science and Game Theory · Computer Science 2020-07-01 Brian Hu Zhang , Tuomas Sandholm

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-07-26 Massimo Bernaschi , Alessandro Celestini , Pasqua D'Ambra , Flavio Vella

Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…

Machine Learning · Computer Science 2020-09-25 Ilay Luz , Meirav Galun , Haggai Maron , Ronen Basri , Irad Yavneh

We present a fast block direct solver for the unified dynamic simulations of power systems. This solver uses a novel Q-learning based method for task scheduling. Unified dynamic simulations of power systems represent a method in which the…

Machine Learning · Computer Science 2021-10-13 Yingshi Chen , Xinli Song , HanYang Dai , Tao Liu , Wuzhi Zhong , Guoyang Wu

We propose a GPU-based distributed optimization algorithm, aimed at controlling optimal power flow in multi-phase and unbalanced distribution systems. Typically, conventional distributed optimization algorithms employed in such scenarios…

Optimization and Control · Mathematics 2023-10-17 Minseok Ryu , Geunyeong Byeon , Kibaek Kim

In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving…

Cryptography and Security · Computer Science 2014-12-05 Hamza Jeljeli