Related papers: A Progressive Statistical Method for Preconditioni…
For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method is also extended to work in connection with Tikhonov…
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,…
This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled…
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…
We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…
We describe a randomized variant of the block conjugate gradient method for solving a single positive-definite linear system of equations. Our method provably outperforms preconditioned conjugate gradient with a broad-class of…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…
The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…
A preconditioning strategy is proposed for the iterative solve of large numbers of linear systems with parameter-dependent matrix and right-hand side which arise during the computation of solution statistics of stochastic elliptic partial…
Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually…
First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is…
This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…
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…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
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 considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
The convergence rates of iterative methods for solving a linear system $\mathbf{A} x = b$ typically depend on the condition number of the matrix $\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…