相关论文: On the preconditioned AOR iterative method for Z-m…

We show that a combination of two simple preprocessing steps would generally improve the conditioning of a homogeneous system of linear inequalities. Our approach is based on a comparison among three different but related notions of…

Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this paper, we demonstrate how preconditioning can circumvent a stringent assumption for sign consistency in…

This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…

We present an efficient preconditioner for linear problems $A x=y$. It guarantees monotonic convergence of the memory-efficient fixed-point iteration for all accretive systems of the form $A = L + V$, where $L$ is an approximation of $A$,…

This article proposes a new class of general linear method with $p=q$ and $r=s=p+1$. The construction of the present method is carried out using order conditions and error minimization subject to $A$- stability constraints. The proposed…

In the context of isogeometric analysis, we consider two discretization approaches that make the resulting stiffness matrix nonsymmetric even if the differential operator is self-adjoint. These are the collocation method and the…

Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

In this paper, we aim at solving the Biot model under stabilized finite element discretizations. To solve the resulting generalized saddle point linear systems, some iterative methods are proposed and compared. In the first method, we apply…

Consider using the right-preconditioned GMRES (AB-GMRES) for obtaining the minimum-norm solution of inconsistent underdetermined systems of linear equations. Morikuni (Ph.D. thesis, 2013) showed that for some inconsistent and…

We apply preconditioning, which is widely used in classical solvers for linear systems $A\textbf{x}=\textbf{b}$, to the variational quantum linear solver. By utilizing incomplete LU factorization as a preconditioner for linear equations…

In this article we present a new multigrid preconditioner for the linear systems arising in the semismooth Newton method solution of certain control-constrained, quadratic distributed optimal control problems. Using a piecewise constant…

Computing the solution of linear systems of equations is invariably the most time consuming task in the numerical solutions of PDEs in many fields of computational science. In this study, we focus on the numerical simulation of…

A technique for computing an ILU preconditioner based on the FAPINV algorithm is presented. We show that this algorithm is well-defined for H-matrices. Moreover, when used in conjunction with Krylov-subspace-based iterative solvers such as…

We focus on inverse preconditioners based on minimizing $F(X) = 1-\cos(XA,I)$, where $XA$ is the preconditioned matrix and $A$ is symmetric and positive definite. We present and analyze gradient-type methods to minimize $F(X)$ on a suitable…

This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…

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…

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 paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…

This paper presents a new stochastic preconditioning approach. For symmetric diagonally-dominant M-matrices, we prove that an incomplete LDL factorization can be obtained from random walks, and used as a preconditioner for an iterative…