Related papers: Preconditioning Parametrized Linear Systems
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…
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…
This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and…
We propose a new method for preconditioning Kaczmarz method by sketching. Kaczmarz method is a stochastic method for solving overdetermined linear systems based on a sampling of matrix rows. The standard approach to speed up convergence of…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
This paper deals with the fast solution of linear systems associated with the mass matrix, in the context of isogeometric analysis. We propose a preconditioner that is both efficient and easy to implement, based on a diagonal-scaled…
In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…
The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system at each time-step. This work develops a fully robust and…
Using the framework of operator or Cald\'{e}ron preconditioning, uniform preconditioners are constructed for elliptic operators of order $2s \in [0,2]$ discretized with continuous finite (or boundary) elements. The cost of the…
Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as…
Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm, has been proposed. The main computational cost of the AIRGA…
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…
An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury…
The hierarchical interpolative factorization for elliptic partial differential equations is a fast algorithm for approximate sparse matrix inversion in linear or quasilinear time. Its accuracy can degrade, however, when applied to strongly…
We show that the mass matrix derived from finite elements can be effectively used as a preconditioner for iteratively solving the linear system arising from finite-difference discretization of the Poisson equation, using the conjugate…
Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…
Linear systems arise in generating samples and in calculating observables in lattice quantum chromodynamics~(QCD). Solving the Hermitian positive definite systems, which are sparse but ill-conditioned, involves using iterative methods, such…