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We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov…

Optimization and Control · Mathematics 2016-10-20 Andrew Knyazev , Alexander Malyshev

Large language model (LLM) training and finetuning are often bottlenecked by limited GPU memory. While existing projection-based optimization methods address this by projecting gradients into a lower-dimensional subspace to reduce optimizer…

Machine Learning · Computer Science 2024-06-26 Aashiq Muhamed , Oscar Li , David Woodruff , Mona Diab , Virginia Smith

Knowledge graph (KG) learning offers a powerful framework for generating new knowledge and making inferences. Training KG embedding can take a significantly long time, especially for larger datasets. Our analysis shows that the gradient…

Machine Learning · Computer Science 2025-05-01 Md Saidul Hoque Anik , Ariful Azad

In this paper, we present a GPU-accelerated direct-sum boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov…

Numerical Analysis · Mathematics 2015-06-12 Weihua Geng , Ferosh Jacob

We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the…

Numerical Analysis · Mathematics 2026-04-22 Mengdi Wang , Yuchen Sun , Bo Zhu

This study investigates computationally efficient algorithms for solving discrete-time infinite-horizon single-agent/multi-agent dynamic models with continuous actions. It shows that we can easily reduce the computational costs by slightly…

General Economics · Economics 2025-02-21 Takeshi Fukasawa

Over the past year, 3D Gaussian Splatting (3DGS) has received significant attention for its ability to represent 3D scenes in a perceptually accurate manner. However, it can require a substantial amount of storage since each splat's…

Computer Vision and Pattern Recognition · Computer Science 2025-04-11 Brent Zoomers , Maarten Wijnants , Ivan Molenaers , Joni Vanherck , Jeroen Put , Lode Jorissen , Nick Michiels

Sparse Matrix-Vector Multiplication (SpMV) is the cornerstone in many iterative workloads, including large-scale graph analytics and sparse iterative solvers. Accelerating SpMV on real-world graphs remains challenging due to highly…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-11 Qi Zhang , Zhengan Yao , Zhenglu Jiang , Zan-Bo Zhang

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…

Numerical Analysis · Mathematics 2023-09-25 Christophe Blondeau , Mehdi Jadoui

We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…

High Energy Physics - Lattice · Physics 2011-02-16 Richard Galvez , Greg van Anders

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

Numerical Analysis · Mathematics 2025-07-22 Nunzio Dimola , Alessandro Coclite , Paolo Zunino

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…

Numerical Analysis · Mathematics 2013-02-01 Pierre Gosselet , Christian Rey , Julien Pebrel

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…

Numerical Analysis · Mathematics 2013-01-14 Chunsheng Feng , Shi Shu , Jinchao Xu , Chen-Song Zhang

In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, requires solving large sparse systems of linear equations…

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

Dictionary training for sparse representations involves dealing with large chunks of data and complex algorithms that determine time consuming implementations. SBO is an iterative dictionary learning algorithm based on constructing unions…

Computer Vision and Pattern Recognition · Computer Science 2014-12-17 Paul Irofti

In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of…

Numerical Analysis · Mathematics 2016-03-08 Meghan O'Connell , Misha E. Kilmer , Eric de Sturler , Serkan Gugercin

Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…

Data Structures and Algorithms · Computer Science 2022-12-16 Thaha Mohammed , Rashid Mehmood

Dynamic 4D Gaussian Splatting (4DGS) effectively extends the high-speed rendering capabilities of 3D Gaussian Splatting (3DGS) to represent volumetric videos. However, the large number of Gaussians, substantial temporal redundancies, and…

Graphics · Computer Science 2026-01-14 Hyeongmin Lee , Kyungjune Baek

Recent advancements in 3D Gaussian Splatting (3DGS) have made a significant impact on rendering and reconstruction techniques. Current research predominantly focuses on improving rendering performance and reconstruction quality using…

Computer Vision and Pattern Recognition · Computer Science 2025-09-18 Yinlong Bai , Hongxin Zhang , Sheng Zhong , Junkai Niu , Hai Li , Yijia He , Yi Zhou

Rotation equivariant graph neural networks, i.e. networks designed to guarantee certain geometric relations between their inputs and outputs, yield state of the art performance on spatial deep learning tasks. They exhibit high data…

Machine Learning · Computer Science 2025-05-12 Vivek Bharadwaj , Austin Glover , Aydin Buluc , James Demmel