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Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for…

Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2022-09-26 Agniva Chowdhury , Gregory Dexter , Palma London , Haim Avron , Petros Drineas

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…

Numerical Analysis · Mathematics 2015-06-18 Qinian Jin , Xiliang Lu

We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…

Exactly Solvable and Integrable Systems · Physics 2015-07-17 Nikolay K. Vitanov , Zlatinka I. Dimitrova , Kaloyan N. Vitanov

We consider the uniqueness of solution (i.e., nonsingularity) of systems of $r$ generalized Sylvester and $\star$-Sylvester equations with $n\times n$ coefficients. After several reductions, we show that it is sufficient to analyze periodic…

Numerical Analysis · Mathematics 2019-06-18 Fernando De Terán , Bruno Iannazzo , Federico Poloni , Leonardo Robol

We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…

Computational Physics · Physics 2016-06-22 Allan Peter Engsig-Karup , Claes Eskilsson , Daniele Bigoni

In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…

Numerical Analysis · Mathematics 2016-02-02 William McLean , Vidar Thomée

The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydrodynamic waves in plasma, nonlinear transverse waves in shallow water and phonon packets…

Numerical Analysis · Mathematics 2019-04-09 Seydi Battal Gazi Karakoc , Samir Kumar Bhowmik

The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…

Atmospheric and Oceanic Physics · Physics 2020-04-22 Jeffrey J. Early , M. Pascale Lelong , K. Shafer Smith

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…

Optimization and Control · Mathematics 2025-10-16 Ling Liang , Qiyuan Pang , Kim-Chuan Toh , Haizhao Yang

Recently, two different proofs for large and intermediate-size solitary waves of the nonlocally dispersive Whitham equation have been presented, using either global bifurcation theory or the limit of waves of large period. We give here a…

Analysis of PDEs · Mathematics 2023-03-27 Mathias Nikolai Arnesen , Mats Ehrnstrom , Atanas G. Stefanov

Using the KAM method, we exhibit some solutions of a finite-dimensional approximation of the Zakharov Hamiltonian formulation of gravity water waves, which are spatially periodic, quasi-periodic in time, and not permanent form travelling…

Chaotic Dynamics · Physics 2007-05-23 Tounsia Benzekri , Ricardo Lima , Michel Vittot

We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.

Analysis of PDEs · Mathematics 2023-08-15 Katrin Grunert , Audun Reigstad

In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous bilinear lattice KP equation, non-autonomous lattice…

Mathematical Physics · Physics 2014-09-17 Songlin Zhao , Wei Feng , Shoufeng Shen , Jun Zhang

The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…

Classical Physics · Physics 2020-02-20 Laurent Vuillon , Denys Dutykh , Francesco Fedele

The present paper makes a connection between collective bosonic states and the exact solutions of the $p_x + ip_y$ pairing Hamiltonian. This makes it possible to investigate the effects of the Pauli principle on the energy spectrum, by…

Strongly Correlated Electrons · Physics 2014-05-07 Mario Van Raemdonck , Stijn De Baerdemacker , Dimitri Van Neck

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…

Numerical Analysis · Mathematics 2026-01-26 Jakob S. Stokke , Kundan Kumar , Florin A. Radu

Salkuyeh proposed the Picard-HSS iteration method to solve the absolute value equation (AVE), which is a class of non-differentiable NP-hard problem. To further improve its performance, a nonlinear HSS-like iteration method is proposed.…

Numerical Analysis · Mathematics 2018-01-03 Mu-Zheng Zhu , Ya-E Qi

The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…

Numerical Analysis · Mathematics 2013-09-24 Anuradha Singh , J. P. Jaiswa

When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…

Numerical Analysis · Mathematics 2023-09-26 Tony Hu , James Bremer