相关论文: A class of inexact block factorization preconditio…
We consider the use of multipreconditioning to solve linear systems when more than one preconditioner is available but the optimal choice is not known. In particular, we consider a selective multipreconditioned GMRES algorithm where we…
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
Incomplete factorization is a widely used preconditioning technique for Krylov subspace methods for solving large-scale sparse linear systems. Its multilevel variants, such as ILUPACK, are more robust for many symmetric or unsymmetric…
Preconditioning for overdetermined least-squares problems has received comparatively little attention, and designing methods that are both effective and memory-efficient remains challenging. We propose a class of ILU-based preconditioners…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
We consider the split-preconditioned FGMRES method in a mixed precision framework, in which four potentially different precisions can be used for computations with the coefficient matrix, application of the left preconditioner, application…
Due to the indefiniteness and poor spectral properties, the discretized linear algebraic system of the vector Laplacian by mixed finite element methods is hard to solve. A block diagonal preconditioner has been developed and shown to be an…
We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid-structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a…
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
We develop eigenvalue bounds for symmetric, block tridiagonal multiple saddle-point linear systems, preconditioned with block diagonal matrices. We extend known results for $3 \times 3$ block systems [Bradley and Greif, IMA J.\ Numer. Anal.…
Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…
Challenging aspects of large-scale turbulent edge simulations in plasma physics include robust nonlinear solvers and efficient preconditioners. This paper presents recent advances in the scalable solution of nonlinear partial differential…
The use of block Krylov subspace methods for computing the solution to a sequence of shifted linear systems using subspace recycling was first proposed in [Soodhalter, SISC 2016], where a recycled shifted block GMRES algorithm (rsbGMRES)…
We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe…
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix…
We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov…
The focus of this work is on the construction and analysis of optimal-order multigrid preconditioners to be used in the Newton-Krylov method for a distributed optimal control problem constrained by the stationary Navier-Stokes equations. As…
We derive nonlinear acceleration methods based on the limited memory BFGS (L-BFGS) update formula for accelerating iterative optimization methods of alternating least squares (ALS) type applied to canonical polyadic (CP) and Tucker tensor…
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…