Related papers: Hermitian Preconditioning for a class of Non-Hermi…
A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
The convergence of the GMRES linear solver is notoriously hard to predict. A particularly enlightening result by [Greenbaum, Pt\'ak, Strako\v{s}, 1996] is that, given any convergence curve, one can build a linear system for which GMRES…
We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present challenging sparse linear systems which are complex…
Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) deals with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in 2004, uses…
We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen-…
In [McDonald, Pestana and Wathen, \textit{SIAM J. Sci. Comput.}, 40 (2018), pp. A1012--A1033], a block circulant preconditioner is proposed for all-at-once linear systems arising from evolutionary partial differential equations, in which…
Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the…
In this study, the $\theta$-method is used for discretizing a class of evolutionary partial differential equations. Then, we transform the resultant all-at-once linear system and introduce a novel one-sided preconditioner, which can be fast…
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…
Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A \in \mathbb{R}^{n \times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners…
In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable coefficient Helmholtz equation including very high frequency problems. The first central idea of this novel approach is to…
GMRES is known to determine a least squares solution of $ A x = b $ where $ A \in R^{n \times n} $ without breakdown for arbitrary $ b \in R^n $, and initial iterate $ x_0 \in R^n $ if and only if $ A $ is range-symmetric, i.e. $ R(A^T) =…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
Stationary iterative methods with a symmetric splitting matrix are performed as inner-iteration preconditioning for Krylov subspace methods. We give conditions such that the inner-iteration preconditioning matrix is definite, and show that…
We present two minimum residual methods for solving sequences of shifted linear systems, the right-preconditioned shifted GMRES and shifted recycled GMRES algorithms which use a seed projection strategy often employed to solve multiple…
This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this…