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We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…

Numerical Analysis · Mathematics 2017-08-08 Robert O'Connor

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

Machine Learning · Statistics 2018-06-18 Pratik Jawanpuria , Bamdev Mishra

We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…

Numerical Analysis · Computer Science 2013-11-14 Richard Peng , Daniel A. Spielman

We present a class of fast subspace tracking algorithms based on orthogonal iterations for structured matrices/pencils that can be represented as small rank perturbations of unitary matrices. The algorithms rely upon an updated data sparse…

Numerical Analysis · Mathematics 2021-04-23 Roberto Bevilacqua , Gianna M. Del Corso , Luca Gemignani

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

Data Structures and Algorithms · Computer Science 2015-01-09 Aditya Bhaskara , Ananda Theertha Suresh , Morteza Zadimoghaddam

The calibration of modern radio interferometers is a significant challenge, specifically at low frequencies. In this perspective, we propose a novel iterative calibration algorithm, which employs the popular sparse representation framework,…

Instrumentation and Methods for Astrophysics · Physics 2016-06-06 Martin Brossard , Mohamed Nabil El Korso , Marius Pesavento , Rémy Boyer , Pascal Larzabal

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…

Machine Learning · Statistics 2011-09-12 S. Derin Babacan , Martin Luessi , Rafael Molina , Aggelos K. Katsaggelos

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…

Machine Learning · Computer Science 2012-12-18 Pablo Sprechmann , Alex M. Bronstein , Guillermo Sapiro

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…

Machine Learning · Statistics 2016-03-02 Milad Kharratzadeh , Mark Coates

Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…

Optimization and Control · Mathematics 2021-08-05 Reka A. Kovacs , Oktay Gunluk , Raphael A. Hauser

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…

Numerical Analysis · Computer Science 2016-06-29 Yuji Nakatsukasa , Tasuku Soma , André Uschmajew

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…

Systems and Control · Electrical Eng. & Systems 2021-05-06 Declan Burke , Airlie Chapman , Iman Shames

Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…

Mathematical Software · Computer Science 2016-08-24 Mathias Jacquelin , Yili Zheng , Esmond Ng , Katherine Yelick

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

Machine Learning · Computer Science 2020-04-14 Biswajit Paria , Chih-Kuan Yeh , Ian E. H. Yen , Ning Xu , Pradeep Ravikumar , Barnabás Póczos

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

Machine Learning · Statistics 2018-10-10 Chendi Huang , Yuan Yao

Linear detectors such as zero forcing (ZF) or minimum mean square error (MMSE) are imperative for large/massive MIMO systems for both the downlink and uplink scenarios. However these linear detectors require matrix inversion which is…

Information Theory · Computer Science 2016-11-15 Vipul Gupta , Abhay Kumar Sah , A. K. Chaturvedi

We consider the task of designing sparse control laws for large-scale systems by directly minimizing an infinite horizon quadratic cost with an $\ell_1$ penalty on the feedback controller gains. Our focus is on an improved algorithm that…

Optimization and Control · Mathematics 2013-12-18 Matt Wytock , J. Zico Kolter

We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the…

Mathematical Software · Computer Science 2021-10-19 Yang Liu , Pieter Ghysels , Lisa Claus , Xiaoye Sherry Li

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

Numerical Analysis · Mathematics 2016-08-12 Sergey Voronin , Dylan Mikesell , Guust Nolet