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This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial…

Numerical Analysis · Mathematics 2024-09-24 Jared L. Aurentz , Vassilis Kalantzis , Yousef Saad

In this paper, we study an efficient algorithm for constructing node sets of high-quality quasi-Monte Carlo integration rules for weighted Korobov, Walsh, and Sobolev spaces. The algorithm presented is a reduced fast successive coordinate…

Numerical Analysis · Mathematics 2020-04-08 Adrian Ebert , Peter Kritzer

We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…

Symbolic Computation · Computer Science 2007-05-23 Wayne Eberly , Mark Giesbrecht , Pascal Giorgi , Arne Storjohann , Gilles Villard

Current bundle adjustment solvers such as the Levenberg-Marquardt (LM) algorithm are limited by the bottleneck in solving the Reduced Camera System (RCS) whose dimension is proportional to the camera number. When the problem is scaled up,…

Computer Vision and Pattern Recognition · Computer Science 2023-02-28 Lei Zhou , Zixin Luo , Mingmin Zhen , Tianwei Shen , Shiwei Li , Zhuofei Huang , Tian Fang , Long Quan

We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the $\ell_1$-norm penalty to filter…

Machine Learning · Computer Science 2023-06-12 Tomojit Ghosh , Michael Kirby , Karim Karimov

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

Machine Learning · Computer Science 2016-03-30 Luc Le Magoarou , Rémi Gribonval

Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this…

Numerical Analysis · Mathematics 2020-10-22 Edwin Chau , Jamie Haddock

Nowadays, several data analysis problems require for complexity reduction, mainly meaning that they target at removing the non-influential covariates from the model and at delivering a sparse model. When categorical covariates are present,…

Statistics Theory · Mathematics 2022-12-21 Lea Kaufmann , Maria Kateri

Sparse prediction with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection…

Methodology · Statistics 2021-12-22 Szymon Nowakowski , Piotr Pokarowski , Wojciech Rejchel

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…

Numerical Analysis · Mathematics 2019-05-24 Minhong Chen , Daniel Kressner

The moment-sum of squares hierarchy by Lasserre has become an established technique for solving polynomial optimization problems. It provides a monotonically increasing series of tight bounds, but has well-known scalability limitations. For…

Optimization and Control · Mathematics 2024-02-09 Daria Shaydurova , Volker Kaibel , Sebastian Sager

Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale…

Numerical Analysis · Mathematics 2023-04-25 Bo Feng , Gang Wu

We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…

Machine Learning · Statistics 2016-11-08 Brian R. Gaines , Hua Zhou

Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…

Data Structures and Algorithms · Computer Science 2025-10-13 Klaus Jansen , Kai Kahler , Lis Pirotton , Malte Tutas

Compute-and-Forward (C&F) has been proposed as an efficient strategy to reduce the backhaul load for the distributed antenna systems. Finding the optimal coefficients in C&F has commonly been treated as a shortest vector problem (SVP),…

Information Theory · Computer Science 2017-04-18 Qinhui Huang , Alister Burr

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for…

Numerical Analysis · Mathematics 2015-12-29 Ruipeng Li , Yuanzhe Xi , Eugene Vecharynski , Chao Yang , Yousef Saad

Integer programming with block structures has received considerable attention recently and is widely used in many practical applications such as train timetabling and vehicle routing problems. It is known to be NP-hard due to the presence…

Optimization and Control · Mathematics 2024-07-01 Rui Wang , Chuwen Zhang , Shanwen Pu , Jianjun Gao , Zaiwen Wen

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…

Numerical Analysis · Computer Science 2010-09-03 Adam C. Zelinski , Vivek K Goyal , Elfar Adalsteinsson

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

Numerical Analysis · Mathematics 2026-05-29 Yonghan Sun , Hou-Duo Qi , Deren Han , Jiaxin Xie

In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…

Numerical Analysis · Mathematics 2024-03-08 Angelo A. Casulli , Igor Simunec