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This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both H\"older smooth and block H\"older smooth. Our analysis applies to objective functions that are…

Optimization and Control · Mathematics 2024-03-14 Leandro Farias Maia , David Huckleberry Gutman

Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…

Machine Learning · Computer Science 2022-12-19 Tiejin Chen , Yicheng Tao

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

Numerical Analysis · Mathematics 2023-04-25 Sergey A. Matveev , Stanislav Budzinskiy

The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…

Numerical Analysis · Mathematics 2022-10-18 Lionel Tondji , Dirk A Lorenz

The Kaczmarz method is an iterative projection scheme for solving con-sistent system $Ax = b$. It is later extended to the inconsistent and ill-posed linear problems. But the classical Kaczmarz method is sensitive to the correlation of the…

Numerical Analysis · Mathematics 2022-10-04 Chuan-gang Kang , Heng Zhou

This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…

Optimization and Control · Mathematics 2026-03-25 Hong Zhu , Xun Qian

The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…

Optimization and Control · Mathematics 2014-03-20 Florian Bugarin , Adrien Bartoli , Didier Henrion , Jean-Bernard Lasserre , Jean-José Orteu , Thierry Sentenac

Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis and…

Data Structures and Algorithms · Computer Science 2017-03-10 Insu Han , Dmitry Malioutov , Haim Avron , Jinwoo Shin

In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…

Numerical Analysis · Mathematics 2023-10-20 Yujun Zhu , Ju Ming , Jie Zhu , Zhongming Wang

In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex…

Optimization and Control · Mathematics 2013-11-27 Peter Richtárik , Martin Takáč

The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are…

Statistics Theory · Mathematics 2023-03-10 Vincent Brault , Antoine Channarond

In this paper, we show that the bundle method can be applied to solve semidefinite programming problems with a low rank solution without ever constructing a full matrix. To accomplish this, we use recent results from randomly sketching…

Optimization and Control · Mathematics 2021-02-02 Lijun Ding , Benjamin Grimmer

The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…

Computational Physics · Physics 2015-05-27 P. A. Belov , E. R. Nugumanov , S. L. Yakovlev

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Numerical Analysis · Mathematics 2019-11-28 N. Benjamin Erichson , Lionel Mathelin , Steven L. Brunton , J. Nathan Kutz

Randomized SVD has become an extremely successful approach for efficiently computing a low-rank approximation of matrices. In particular the paper by Halko, Martinsson, and Tropp (SIREV 2011) contains extensive analysis, and has made it a…

Numerical Analysis · Mathematics 2020-09-25 Yuji Nakatsukasa

The randomized projection (RP) method is a simple iterative scheme for solving linear feasibility problems and has recently gained popularity due to its speed and low memory requirement. This paper develops an accelerated variant of the…

Optimization and Control · Mathematics 2022-11-21 Lin Zhu , Yuan Lei , Jiaxin Xie

In the iterative solution of dense linear systems from boundary integral equations or systems involving kernel matrices, the main challenges are the expensive matrix-vector multiplication and the storage cost which are usually tackled by…

Numerical Analysis · Mathematics 2018-11-13 Xin Xing , Edmond Chow

Combined optimization problems that couple data-fidelity and regularization terms arise naturally in a wide range of inverse problems. In this paper, we study an adaptive randomized averaging block extended Bregman-Kaczmarz (aRABEBK) method…

Numerical Analysis · Mathematics 2026-01-19 Zeyu Dong , Aqin Xiao , Guojian Yin , Junfeng Yin

This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Runge-Kutta method with repeated randomized low-rank…

Numerical Analysis · Mathematics 2024-09-11 Hei Yin Lam , Gianluca Ceruti , Daniel Kressner

This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…

Numerical Analysis · Mathematics 2024-10-30 Yatian Wang , Hua Xiang , Chi Zhang , Songling Zhang