Related papers: Two recursive GMRES-type methods for shifted linea…
This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied…
LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior…
Inference amortization methods share information across multiple posterior-inference problems, allowing each to be carried out more efficiently. Generally, they require the inversion of the dependency structure in the generative model, as…
Generative sequence modeling faces a fundamental tension between the expressivity of Transformers and the efficiency of linear sequence models. Existing efficient architectures are theoretically bounded by shallow, single-step linear…
We explore the use of flexible GMRES as an outer wrapper for sketched GMRES. Building on a new bound for the residual of FGMRES in terms of the residual of the preconditioner, we derive a practical randomized solver that requires very…
We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…
This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial guesses over a sequence of linear systems with…
In this contribution, we study the numerical behavior of the Generalized Minimal Residual (GMRES) method for solving singular linear systems. It is known that GMRES determines a least squares solution without breakdown if the coefficient…
This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence…
We investigate fast direct methods for solving systems of the form (B + G)x = y, where B is a limited-memory BFGS matrix and G is a symmetric positive-definite matrix. These systems, which we refer to as shifted L-BFGS systems, arise in…
As the need for computational power and efficiency rises, parallel systems become increasingly popular among various scientific fields. While multiple core-based architectures have been the center of attention for many years, the rapid…
We propose a block Krylov subspace version of the GCRO-DR method proposed in [Parks et al.; SISC 2005], which is an iterative method allowing for the efficient minimization of the the residual over an augmented Krylov subspace. We offer a…
Algorithms for data assimilation try to predict the most likely state of a dynamical system by combining information from observations and prior models. Variational approaches, such as the weak-constraint four-dimensional variational data…
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…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
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…
We present a method for projecting an input image into the space of a class-conditional generative neural network. We propose a method that optimizes for transformation to counteract the model biases in generative neural networks.…