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This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small…

Numerical Analysis · Mathematics 2020-09-01 Nilima Nigam , Sara Pollock

Computer simulations are invaluable tools for scientific discovery. However, accurate simulations are often slow to execute, which limits their applicability to extensive parameter exploration, large-scale data analysis, and uncertainty…

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…

Optimization and Control · Mathematics 2019-10-22 Tobias Sutter , David Sutter , Peyman Mohajerin Esfahani , John Lygeros

In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…

Symbolic Computation · Computer Science 2019-01-01 Jin-San Cheng , Xiaojie Dou , Junyi Wen

We perform an extrapolative analysis of "fast-growth" free-energy-difference (DF) estimates of a computer-modeled, fully-solvated ethane<->methanol transformation. The results suggest that extrapolation can greatly reduce the systematic…

Chemical Physics · Physics 2007-05-23 Daniel M. Zuckerman , Thomas B. Woolf

In April 2025 GMV announced a competition for finding the best method to solve a particular polynomial system over a finite field. In this paper we provide a method for solving the given equation system significantly faster than what is…

Computational Complexity · Computer Science 2026-03-06 Àngela Barbero , Ragnar Freij-Hollanti , Camilla Hollanti , Håvard Raddum , Øyvind Ytrehus , Morten Øygarden

We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…

Optimization and Control · Mathematics 2020-06-03 Le Thi Khanh Hien , Nicolas Gillis , Panagiotis Patrinos

In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…

Computational Physics · Physics 2021-06-30 Igor Semenikhin

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

Machine Learning · Computer Science 2023-05-17 Min Zhu , Handi Zhang , Anran Jiao , George Em Karniadakis , Lu Lu

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…

Numerical Analysis · Mathematics 2023-01-31 Sohei Arisaka , Qianxiao Li

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Numerical Analysis · Mathematics 2016-05-30 Oliver J. D. Barrowclough , Tor Dokken

We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…

Numerical Analysis · Mathematics 2024-02-28 T. Chaumont-Frelet

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

Numerical Analysis · Mathematics 2026-01-09 Tomas Teijeiro , Pouria Behnoudfar , Jamie M. Taylor , David Pardo , Victor M. Calo

The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…

Numerical Analysis · Mathematics 2024-03-19 Alessandra Vizzaccaro , Giorgio Gobat , Attilio Frangi , Cyril Touzé

We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…

Numerical Analysis · Mathematics 2008-05-21 James Demmel , Ioana Dumitriu , Olga Holtz , Plamen Koev

Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…

Symbolic Computation · Computer Science 2010-12-01 Xiao-Shan Gao , Zhenyu Huang

Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…

Numerical Analysis · Mathematics 2020-02-28 Julius Reiss

In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…

Numerical Analysis · Mathematics 2022-08-15 Santiago Badia , Eric Neiva , Francesc Verdugo

Channel estimation and extrapolation are fundamental issues in MIMO communication systems. In this paper, we proposed the quasi-Newton orthogonal matching pursuit (QNOMP) approach to overcome these issues with high efficiency while…

Signal Processing · Electrical Eng. & Systems 2024-11-12 Yi Zeng , Mingguang Han , Xiaoguang Li , Tiejun Li

We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…

Numerical Analysis · Mathematics 2020-02-11 Alexander Zaitzeff , Selim Esedoglu , Krishna Garikipati