The Generalized Minimum Residual (GMRES) method is a popular Krylov subspace projection method for solving a nonsymmetric linear system of equations. On modern computers, communication is becoming increasingly expensive compared to arithmetic operations, and a communication-avoiding variant (CA-GMRES) may improve the performance of GMRES. To further enhance the performance of CAGMRES, in this p...

On the Asymptotic Linear Convergence Speed of Anderson Acceleration, Nesterov and Nonlinear GMRES

In this paper we show how the properties of integral operators and their approximations are reeected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden's method and we present some comparisons of the two methods ...

We study the convergence of GMRES for linear algebraic systems with normal matrices. In particular, we explore the standard bound based on a min-max approximation problem on the discrete set of the matrix eigenvalues. This bound is sharp, i.e. it is attainable by the GMRES residual norm. The question is how to evaluate or estimate the standard bound, and if it is possible to characterize the GM...

More recently, Beik and Salkuyeh [F. P. A. Beik and D. K. Salkuyeh, On the global Krylov subspace methods for solving general coupled matrix equations, Computers and Mathematics with Applications, 62 (2011) 4605–4613] have presented the Gl-FOM and Gl-GMRES algorithms for solving the general coupled linear matrix equations. In this paper, two new algorithms called weighted Gl-FOM (WGl-FOM) and w...

The Generalized Minimal Residual (GMRES) method is one of the most popular algorithms for the solution of large, sparse and unsymmetric linear systems of equations Ax = b [6]. The idea behind the GMRES is to construct an orthogonal matrix Vk such that its k columns span a Krylov subspace. The time and memory costs of computing Vk are proportional to k, so that, as k grows, the computational cos...

[1] We introduce the preconditioned generalized minimum residual (GMRES) method, along with an outer loop (OL) iteration to solve the sea-ice momentum equation. The preconditioned GMRES method is the linear solver. GMRES together with the OL is used to solve the nonlinear momentum equation. The GMRES method has low storage requirements, and it is computationally efficient and parallelizable. It...

The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. This paper discusses application of the GMRES method to the solution of large linear systems of equations that arise from the discretization of linear ill-posed problems. These linear systems are severely ill-conditioned and are referred to as discrete ill...

Consider using the right-preconditioned GMRES (AB-GMRES) for obtaining minimum-norm solution of inconsistent underdetermined systems linear equations. Morikuni (Ph.D. thesis, 2013) showed that some and ill-conditioned problems, iterates may diverge. This is mainly because Hessenberg matrix in method becomes very so backward substitution resulting triangular system numerically unstable. We propo...

استهدف البحث الحالي تقصي الفروق في القدرة على حل المشكلات لدى طلاب المرحلة الثانوية تبعاً لبعض المتغيرات الديمغرافية (النوع – التخصص الدراسي نوع المدرسة)،