Related papers: Techniques for Accelerating the Convergence of Res…

Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarised as minimising the residuum over a suitable Krylov subspace. It is shown that using the…

Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…

In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…

This paper presents a novel neural network training approach for faster convergence and better generalization abilities in deep reinforcement learning. Particularly, we focus on the enhancement of training and evaluation performance in…

We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…

In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward…

Solving a large-scale system of linear equations is a key step at the heart of many algorithms in machine learning, scientific computing, and beyond. When the problem dimension is large, computational and/or memory constraints make it…

Although recent deep learning methods, especially generative models, have shown good performance in fast magnetic resonance imaging, there is still much room for improvement in high-dimensional generation. Considering that internal…

We consider nonlinear GMRES (NGMRES) as an acceleration technique for the Navier-Stokes Picard iteration, a direction that has not previously been explored. We identify the optimal norm for the least squares optimization problem arising in…

Prompt engineering is critical for the development of LLM-based applications. However, it is usually done manually in a "trial and error" fashion that can be time consuming, ineffective, and sub-optimal. Even for the prompts which seemingly…

Model merging provides a compelling paradigm for integrating specialized expertise into a unified multi-task model, a goal that aligns naturally with the sequential knowledge acquisition in continual learning (CL). However, the requirement…

An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…

Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…

This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…

When reconstructing images from noisy measurements, such as in medical scans or scientific imaging, we face an inverse problem: recovering an unknown image from indirect, corrupted observations. These problems are typically ill-posed,…

Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…

We propose GRGS, a generalizable and relightable 3D Gaussian framework for high-fidelity human novel view synthesis under diverse lighting conditions. Unlike existing methods that rely on per-character optimization or ignore physical…

The Circumcentered Reflection Method (CRM) is a recently developed projection method for solving convex feasibility problems. It offers preferable convergence properties compared to classic methods such as the Douglas-Rachford and the…

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…