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In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…

Optimization and Control · Mathematics 2023-03-06 Kareem T. Elgindy

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 asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…

Mathematical Physics · Physics 2009-01-15 Katherine M. Robertson , Nasser Saad

In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…

Numerical Analysis · Mathematics 2023-07-25 Sean Hon , Jiamei Dong , Stefano Serra-Capizzano

The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…

Numerical Analysis · Mathematics 2014-09-17 Lexing Ying

In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…

Optimization and Control · Mathematics 2021-12-21 Jianchao Bai , Deren Han , Hao Sun , Hongchao Zhang

We introduce a two-parameter version of the two-step scale-splitting iteration method, called TTSCSP, for solving a broad class of complex symmetric system of linear equations. We present some conditions for the convergence of the method.…

Numerical Analysis · Mathematics 2018-02-06 Davod Khojasteh Salkuyeh , Tahereh Salimi Siahkolaei

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Numerical Analysis · Mathematics 2019-07-08 Ashish Kumar Nandi , Jajati Keshari Sahoo , Debasisha Mishra

We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation,…

Optimization and Control · Mathematics 2019-09-10 Jose S. Rodriguez , Carl D. Laird , Victor M. Zavala

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…

Optimization and Control · Mathematics 2015-01-20 Giorgos Stathopoulos , Milan Korda , Colin N. Jones

We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…

Optimization and Control · Mathematics 2019-12-02 Mattias Fält , Pontus Giselsson

This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…

Numerical Analysis · Mathematics 2021-03-11 Jürgen Dölz , Olena Palii , Matthias Schlottbom

This paper presents fast solvers for linear systems arising from the discretization of fractional nonlinear Schr\"odinger equations with Riesz derivatives and attractive nonlinearities. These systems are characterized by complex symmetry,…

Numerical Analysis · Mathematics 2024-10-07 Chao Chen , Xi Yang , Fei-Yan Zhang

This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…

Numerical Analysis · Mathematics 2024-04-10 Juan Zhang , Yiyi Luo

By applying the linearly implicit conservative difference scheme proposed in [D.-L. Wang, A.-G. Xiao, W. Yang. J. Comput. Phys. 2014;272:670-681], the system of repulsive space fractional coupled nonlinear Schr\"odinger equations leads to a…

Numerical Analysis · Mathematics 2024-10-18 Fei-Yan Zhang , Xi Yang , Chao Chen

This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…

Numerical Analysis · Mathematics 2019-09-19 Zhiqiang Cai , Shuhao Cao , Robert D. Falgout

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

Numerical Analysis · Mathematics 2020-08-28 Sana Keita , Abdelaziz Beljadid , Yves Bourgault

The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…

Optimization and Control · Mathematics 2024-12-30 Soodeh Habibi , Michal Kocvara , Michael Stingl

A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new…

Numerical Analysis · Mathematics 2009-12-04 Sapto W. Indratno , A. G. Ramm

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

Numerical Analysis · Mathematics 2024-04-24 Fatemeh P. A. Beik , Michele Benzi , Mehdi Najafi-Kalyani