Related papers: A framework for deflated and augmented Krylov subs…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
Recently, enlarged Krylov subspace methods, that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration based on the domain decomposition of the graph of A, were introduced in the aim of reducing communication…
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…
In this paper, we apply acceleration to the inverse-free preconditioned Krylov subspace method introduced by Golub and Ye, which solves the symmetric generalized eigenvalue problem for the algebraically smallest eigenvalue. As the method is…
High-quality reconstructions of signals and images with sharp edges are needed in a wide range of applications. To overcome the large dimensionality of the parameter space and the complexity of the regularization functional,…
Model-based reconstruction plays a key role in compressed sensing (CS) MRI, as it incorporates effective image regularizers to improve the quality of reconstruction. The Plug-and-Play and Regularization-by-Denoising frameworks leverage…
Krylov subspace methods are linear solvers based on matrix-vector multiplications and vector operations. While easily parallelizable, they are sensitive to rounding errors and may experience convergence issues. ILU(0), an incomplete LU…
New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, non-Hermitian linear systems. These bounds are given for the case when the Hermitian part of the coefficient matrix is…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric…
In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with $hp$-refinement. These preconditioners are based on the decomposition of the DG finite element space…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment or blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale…
In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on…
Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…