Related papers: Preconditioning complex symmetric linear systems
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
This article is concerned with the question of constructing effcient multigrid preconditioners for the linear systems arising when applying semismooth Newton methods to large-scale linear-quadratic optimization problems constrained by…
We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues…
Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of…
In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symmetric linear systems…
We revisit the Hierarchical Poincar\'e-Steklov (HPS) method in a preconditioned iterative setting for variable-coefficient Helmholtz problems with impedance boundary conditions. HPS is commonly presented as a direct solver based on nested…
The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely…
In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…
Techniques based on $k$-th order Hodge Laplacian operators $L_k$ are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplicial complexes. In all of them, it is required to solve a…
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…
In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for $K \times N$ sub-systems connected in a two-dimensional (2D) grid…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…
The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…
In this paper preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of SR1 and BFGS low-rank…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of…