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When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

Optimization and Control · Mathematics 2026-05-05 Xuemei Chen , Owen Deen

Majorization-minimization (MM) is a standard iterative optimization technique which consists in minimizing a sequence of convex surrogate functionals. MM approaches have been particularly successful to tackle inverse problems and…

Applications · Statistics 2018-08-01 Yousra Bekhti , Felix Lucka , Joseph Salmon , Alexandre Gramfort

We propose a new fast randomized algorithm for interpolative decomposition of matrices which utilizes CountSketch. We then extend this approach to the tensor interpolative decomposition problem introduced by Biagioni et al. (J. Comput.…

Numerical Analysis · Mathematics 2024-12-20 Osman Asif Malik , Stephen Becker

Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…

Optimization and Control · Mathematics 2016-12-22 Ketan Rajawat , Sandeep Kumar

Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…

Numerical Analysis · Mathematics 2021-11-16 Eda Oktay , Erin Carson

High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…

Numerical Analysis · Mathematics 2024-06-28 Jakob Vandergrift , Matthew J. Zahr

We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…

Optimization and Control · Mathematics 2017-09-21 Jason E. Hicken , Pengfei Meng , Alp Dener

Recent advances in random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing…

Data Structures and Algorithms · Computer Science 2016-03-24 Marco Genuzio , Giuseppe Ottaviano , Sebastiano Vigna

This article is concerned with the question of constructing effcient multigrid preconditioners for the linear systems arising when applying semismooth Newton methods to large-scale linear-quadratic optimization problems constrained by…

Numerical Analysis · Mathematics 2013-11-08 Andrei Draganescu

Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and…

Numerical Analysis · Mathematics 2025-08-21 Andrew J. Higgins , Erik G. Boman , Ichitaro Yamazaki

Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…

Matrices have become essential data representations for many large-scale problems in data analytics, and hence matrix sketching is a critical task. Although much research has focused on improving the error/size tradeoff under various…

Data Structures and Algorithms · Computer Science 2015-01-27 Amey Desai , Mina Ghashami , Jeff M. Phillips

Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES)…

Numerical Analysis · Mathematics 2021-11-09 Keiichi Morikuni

Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…

Numerical Analysis · Mathematics 2024-04-24 Steffen Börm

Additive smooth models, such as Generalized additive models (GAMs) of location, scale, and shape (GAMLSS), are a popular choice for modeling experimental data. However, software available to fit such models is usually not tailored…

Methodology · Statistics 2025-06-17 Joshua Krause , Jelmer P. Borst , Jacolien van Rij

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

Optimization and Control · Mathematics 2021-12-09 Han Wang , James Anderson

In this paper, we propose a novel adaptive stochastic extended iterative method, which can be viewed as an improved extension of the randomized extended Kaczmarz (REK) method, for finding the unique minimum Euclidean norm least-squares…

Numerical Analysis · Mathematics 2025-09-23 Yun Zeng , Deren Han , Yansheng Su , Jiaxin Xie

We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an oracle access to a stochastic estimate of the Hessian matrix. The oracle model includes…

Optimization and Control · Mathematics 2022-11-29 Sen Na , Michał Dereziński , Michael W. Mahoney

We propose a preconditioner that can accelerate the rate of convergence of the Multiple Shooting Shadowing (MSS) method. This recently proposed method can be used to compute derivatives of time-averaged objectives (also known as…

Numerical Analysis · Mathematics 2019-10-02 Karim Shawki , George Papadakis

Reconstructing high-quality images with sharp edges requires the use of edge-preserving constraints in the regularized form of the inverse problem. The use of the $\ell_q$-norm on the gradient of the image is a common such constraint. For…

Numerical Analysis · Mathematics 2023-09-28 Mirjeta Pasha , Eric de Sturler , Misha E. Kilmer