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Deterministic and randomized, row-action and column-action linear solvers have become increasingly popular owing to their simplicity, low computational and memory complexities, and ease of composition with other techniques. Moreover, in…

Numerical Analysis · Mathematics 2021-04-28 Vivak Patel , Mohammad Jahangoshahi , Daniel Adrian Maldonado

Large-scale linear systems, $Ax=b$, frequently arise in practice and demand effective iterative solvers. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized…

Numerical Analysis · Mathematics 2024-08-26 El Houcine Bergou , Soumia Boucherouite , Aritra Dutta , Xin Li , Anna Ma

While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…

Numerical Analysis · Mathematics 2018-03-20 Babak Maboudi Afkham , Jan S. Hesthaven

The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a modified Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e. the equations within the system are…

Numerical Analysis · Mathematics 2019-04-12 Chinmay Hegde , Fritz Keinert , Eric S. Weber

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

Numerical Analysis · Mathematics 2021-05-19 Tizian Wenzel , Gabriele Santin , Bernard Haasdonk

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

This paper addresses a complex parallel machine scheduling problem with jobs divided into operations and operations grouped in families. Non-anticipatory family setup times are held at the beginning of each batch, defined by the combination…

Optimization and Control · Mathematics 2021-02-12 Davi Mecler , Victor Abu-Marrul , Rafael Martinelli , Arild Hoff

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

Numerical Analysis · Mathematics 2023-12-13 Johannes J. Brust , Michael A. Saunders

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…

Machine Learning · Computer Science 2018-02-12 Di Wang , Jinhui Xu

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

Machine Learning · Computer Science 2019-06-06 Dennis Wei , Sanjeeb Dash , Tian Gao , Oktay Günlük

This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during…

The Kaczmarz algorithm is a well known iterative method for solving overdetermined linear systems. Its randomized version yields provably exponential convergence in expectation. In this paper, we propose two new methods to speed up the…

Numerical Analysis · Computer Science 2016-08-02 Tengfei Ma

The randomized Kaczmarz method and its accelerated variants are a powerful class of iterative methods for solving large-scale linear systems, offering guaranteed convergence with low per-iteration cost. However, their numerical stability…

Numerical Analysis · Mathematics 2026-05-19 Michał Dereziński , Ethan N. Epperly , Deanna Needell , Alexander Xue

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Machine Learning · Computer Science 2022-10-04 Ayano Kaneda , Osman Akar , Jingyu Chen , Victoria Kala , David Hyde , Joseph Teran

Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…

Machine Learning · Computer Science 2025-11-21 Alan Yufei Dong , Jihao Andreas Lin , José Miguel Hernández-Lobato

The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation. In this work we extend this result and show that the recently proposed Randomized Sparse Kaczmarz method for…

Optimization and Control · Mathematics 2016-10-11 Frank Schöpfer , Dirk A. Lorenz

Randomized iterative algorithms have recently been proposed to solve large-scale linear systems. In this paper, we present a simple randomized extended block Kaczmarz algorithm that exponentially converges in the mean square to the unique…

Numerical Analysis · Mathematics 2020-07-09 Kui Du , Wutao Si , Xiaohui Sun

In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…

Optimization and Control · Mathematics 2025-04-03 Lionel Tondji , Dirk A. Lorenz , Ion Necoara

The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations Ax=b. The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution…

Numerical Analysis · Mathematics 2015-06-24 Deanna Needell , Ran Zhao , Anastasios Zouzias

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

Functional Analysis · Mathematics 2012-10-26 Eric Cances , Virginie Ehrlacher , Tony Lelievre