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Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme…

Numerical Analysis · Mathematics 2022-05-18 Peter Kunkel , Volker Mehrmann

Four-variable-independent-regression localization losses, such as Smooth-$\ell_1$ Loss, are used by default in modern detectors. Nevertheless, this kind of loss is oversimplified so that it is inconsistent with the final evaluation metric,…

Computer Vision and Pattern Recognition · Computer Science 2021-12-06 Hanyang Peng , Shiqi Yu

Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the…

Numerical Analysis · Mathematics 2021-10-07 Ben S. Southworth , Oliver Krzysik , Will Pazner

In this paper, we study a parallel-in-time (PinT) algorithm for all-at-once system from a non-local evolutionary equation with weakly singular kernel where the temporal term involves a non-local convolution with a weakly singular kernel and…

Numerical Analysis · Mathematics 2021-03-17 Xue-lei Lin , Michael K. Ng , Yajing Zhi

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the…

Algebraic Geometry · Mathematics 2016-01-05 Jonathan D. Hauenstein , Bernard Mourrain , Agnes Szanto

We consider the quasilinear magneto-quasistatic field equations that arise in the simulation of low-frequency electromagnetic devices coupled to electrical circuits. Spatial discretization of these equations on 3D domains using the finite…

Numerical Analysis · Mathematics 2024-11-22 Johanna Kerler-Back , Timo Reis , Tatjana Stykel

Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of…

Systems and Control · Electrical Eng. & Systems 2026-02-16 Mohammed Adib Oumer , Vishnu Murali , Majid Zamani

We provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint based solution of partial differential equation (PDE) constrained optimization. This…

Optimization and Control · Mathematics 2020-05-28 Oana Marin , Emil Constantinescu , Barry Smith

Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe…

Mathematical Software · Computer Science 2022-02-10 Yingbo Ma , Shashi Gowda , Ranjan Anantharaman , Chris Laughman , Viral Shah , Chris Rackauckas

The design of iterative linear precoding is recently challenged by extremely large aperture array (ELAA) systems, where conventional preconditioning techniques could hardly improve the channel condition. In this paper, it is proposed to…

Signal Processing · Electrical Eng. & Systems 2023-01-27 Jinfei Wang , Yi Ma , Na Yi , Rahim Tafazolli

In this paper, a new data-adaptive method, called DAIS (Data Adaptive ISolation), is introduced for the estimation of the number and the location of change-points in a given data sequence. The proposed method can detect changes in various…

Methodology · Statistics 2025-06-24 Andreas Anastasiou , Sophia Loizidou

Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where…

Methodology · Statistics 2022-08-19 Nan Zhang , Muye Nanshan , Jiguo Cao

We propose a new method for preconditioning Kaczmarz method by sketching. Kaczmarz method is a stochastic method for solving overdetermined linear systems based on a sampling of matrix rows. The standard approach to speed up convergence of…

Numerical Analysis · Computer Science 2019-03-06 Alexandr Katrutsa , Ivan Oseledets

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…

Numerical Analysis · Mathematics 2023-10-19 Yan Cheng , Xi Yang

This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the…

Optimization and Control · Mathematics 2023-08-07 Xin-long Luo , Hang Xiao , Sen Zhang

Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…

Data Structures and Algorithms · Computer Science 2024-01-02 Markus Anders , Pascal Schweitzer , Mate Soos

This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. In this work, we consider the trapezoidal family of schemes for…

Numerical Analysis · Computer Science 2015-05-13 K. B. Nakshatrala , A. Prakash , K. D. Hjelmstad

A matrix framework is presented for the solution of ODEs, including initial-, boundary and inner-value problems. The framework enables the solution of the ODEs for arbitrary nodes. There are four key issues involved in the formulation of…

Numerical Analysis · Mathematics 2013-04-19 Matthew Harker , Paul O'Leary

Deep equilibrium networks (DEQs) are a new class of models that eschews traditional depth in favor of finding the fixed point of a single nonlinear layer. These models have been shown to achieve performance competitive with the…

Machine Learning · Computer Science 2021-06-29 Shaojie Bai , Vladlen Koltun , J. Zico Kolter

We extend the index-aware model-order reduction method to systems of nonlinear differential-algebraic equations with a special nonlinear term f(Ex), where E is a singular matrix. Such nonlinear differential-algebraic equations arise, for…

Numerical Analysis · Mathematics 2020-02-25 Nicodemus Banagaaya , Giuseppe Ali , Sara Grundel , Peter Benner