Related papers: Krylov Methods for Low-Rank Regularization

We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…

Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include the computation of inner-products, which become costly when the number of…

Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…

For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…

This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…

This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or…

In this paper we develop flexible Krylov methods for efficiently computing regularized solutions to large-scale linear inverse problems with an $\ell_2$ fit-to-data term and an $\ell_p$ penalization term, for $p\geq 1$. First we approximate…

Flexible Krylov methods are a common standpoint for inverse problems. In particular, they are used to address the challenges associated with explicit variational regularization when it goes beyond the two-norm, for example involving an…

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…

This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…

This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…

Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…

Low-rank Krylov methods are one of the few options available in the literature to address the numerical solution of large-scale general linear matrix equations. These routines amount to well-known Krylov schemes that have been equipped with…

We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…

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…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…

Second-order optimization methods, such as cubic regularized Newton methods, are known for their rapid convergence rates; nevertheless, they become impractical in high-dimensional problems due to their substantial memory requirements and…