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Related papers: Exploiting variable precision in GMRES

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In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…

Information Theory · Computer Science 2022-01-13 Xiao Lv , Wei Cui , Yulong Liu

An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…

Numerical Analysis · Mathematics 2022-05-13 Sören Bartels , Andrea Bonito , Philipp Tscherner

We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly…

Machine Learning · Statistics 2017-09-12 Xiaowei Zhang , Xudong Shi , Yu Sun , Li Cheng

Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…

Machine Learning · Computer Science 2021-10-04 Kai Jia , Martin Rinard

Motivated by the extensive application of approximate gradients in machine learning and optimization, we investigate inexact subgradient methods subject to persistent additive errors. Within a nonconvex semialgebraic framework, assuming…

Optimization and Control · Mathematics 2025-05-14 Jérôme Bolte , Tam Le , Éric Moulines , Edouard Pauwels

We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the…

Computational Physics · Physics 2019-01-18 Emilio Martínez-Pañeda

We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method…

Numerical Analysis · Mathematics 2023-05-03 Niall Bootland , Vandana Dwarka , Pierre Jolivet , Victorita Dolean , Cornelis Vuik

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

We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…

Symbolic Computation · Computer Science 2018-02-08 Daniel S. Roche

The objective of this publication is to reduce the sensitivity of iterative equation solvers on the initial value. To this end, at the hand of Newton's method, we exemplify how to reformulate the initial problem by means of a set of…

Numerical Analysis · Mathematics 2023-11-30 Alexander Herzog

An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with…

Machine Learning · Computer Science 2018-06-11 Yang Song , Jiaming Song , Stefano Ermon

IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…

Computational Geometry · Computer Science 2021-09-20 Walter F. Mascarenhas

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

Numerical Analysis · Mathematics 2024-04-03 Phillip Semler , Martin Weiser

Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…

Numerical Analysis · Mathematics 2023-07-04 Nils Kohl , Stephen F. McCormick , Rasmus Tamstorf

In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, one seeks to determine the number of multiscale basis…

Numerical Analysis · Mathematics 2015-09-21 Eric T. Chung , Wing Tat Leung , Sara Pollock

Datasets with missing values are very common on industry applications, and they can have a negative impact on machine learning models. Recent studies introduced solutions to the problem of imputing missing values based on deep generative…

Machine Learning · Computer Science 2019-02-28 Ramiro D. Camino , Christian A. Hammerschmidt , Radu State

A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…

Numerical Analysis · Mathematics 2011-08-24 Qingshan Chen , Max Gunzburger

This paper presents a goal-oriented a posteriori error estimation framework for linear functionals in the stabilized finite element discretization of the stationary convection-diffusion-reaction (CDR) equation. The theoretical framework for…

Numerical Analysis · Mathematics 2025-05-07 Sheraz Ahmed Khan , Ramon Codina , Hauke Gravenkamp

In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…

Statistics Theory · Mathematics 2017-07-31 Samuel Balmand , Arnak S. Dalalyan

This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…

Systems and Control · Electrical Eng. & Systems 2025-04-11 Bowen Song , Chenxuan Wu , Andrea Iannelli
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