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Related papers: Sketching for Motzkin's Iterative Method for Linea…

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Recently proposed adaptive Sketch & Project (SP) methods connect several well-known projection methods such as Randomized Kaczmarz (RK), Randomized Block Kaczmarz (RBK), Motzkin Relaxation (MR), Randomized Coordinate Descent (RCD), Capped…

Numerical Analysis · Mathematics 2020-12-25 Md Sarowar Morshed , Sabbir Ahmad , Md Noor-E-Alam

Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully…

Numerical Analysis · Computer Science 2014-07-22 Tim Wallace , Ali Sekmen

High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…

Machine Learning · Computer Science 2017-08-07 Yangchen Pan , Erfan Sadeqi Azer , Martha White

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…

Numerical Analysis · Computer Science 2014-06-12 Huan Wang , Christos Boutsidis , Edo Liberty , Daniel Hsu

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

We present an integral framework for training sketch simplification networks that convert challenging rough sketches into clean line drawings. Our approach augments a simplification network with a discriminator network, training both…

Computer Vision and Pattern Recognition · Computer Science 2017-03-28 Edgar Simo-Serra , Satoshi Iizuka , Hiroshi Ishikawa

Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. In this paper we address the application of CS to the scenario of progressive acquisition of 2D visual…

Information Theory · Computer Science 2014-03-06 Giulio Coluccia , Enrico Magli

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin…

Numerical Analysis · Mathematics 2011-02-15 Yonina C. Eldar , Deanna Needell

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…

Methodology · Statistics 2015-06-22 Clément Gilavert , Saïd Moussaoui , Jérôme Idier

Among recent developments centered around Randomized Kaczmarz (RK), a row-sampling iterative projection method for large-scale linear systems, several adaptions to the method have inspired faster convergence. Focusing solely on…

Numerical Analysis · Mathematics 2026-03-03 James Nguyen , Oleg Presnyakov , Adityakrishnan Radhakhrishnan

In this paper, we propose and analyze iterative method based on projection techniques to solve a non-singular linear system Ax = b. In particular, for a given positive integer m, m-dimensional successive projection method (mD-SPM) for…

Numerical Analysis · Mathematics 2020-03-12 Ashif Mustafa , Manideepa Saha

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

Machine Learning · Computer Science 2024-03-12 Kaiwen Wu , Jonathan Wenger , Haydn Jones , Geoff Pleiss , Jacob R. Gardner

Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian…

Machine Learning · Computer Science 2026-03-20 Ali Saheb Pasand , Johan Obando-Ceron , Aaron Courville , Pouya Bashivan , Pablo Samuel Castro

In this technical report we present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image…

Numerical Analysis · Mathematics 2012-04-03 Deanna Needell , Rachel Ward

We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…

Machine Learning · Statistics 2021-11-02 Diego Granziol , Xingchen Wan , Samuel Albanie , Stephen Roberts

Thanks to its great potential in reducing both computational cost and memory requirements, combining sketching and Krylov subspace techniques has attracted a lot of attention in the recent literature on projection methods for linear…

Numerical Analysis · Mathematics 2024-06-12 Davide Palitta , Marcel Schweitzer , Valeria Simoncini

Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…

Numerical Analysis · Mathematics 2022-04-07 Gong Rongfang , Huang Qin

This paper proposes a sketching strategy based on spherical designs, which is applied to the classical spherical basis function approach for massive spherical data fitting. We conduct theoretical analysis and numerical verifications to…

Machine Learning · Computer Science 2023-03-09 Shao-Bo Lin , Di Wang , Ding-Xuan Zhou

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 Sampling Kaczmarz Motzkin (SKM) algorithm is a generalized method for solving large scale linear systems of inequalities. Having its root in the relaxation method of Agmon, Schoenberg, and Motzkin and the randomized Kaczmarz method, SKM…

Optimization and Control · Mathematics 2022-08-16 Md Sarowar Morshed , Md Saiful Islam , Md. Noor-E-Alam