Related papers: Optimal Krylov On Average
We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…
We develop a spectral low-mode reduced solver for second-order elliptic boundary value problems with spatially varying diffusion coefficients. The approach projects standard finite difference or finite element discretization onto a global…
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…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Krylov subspace methods are among the most extensively studied early fault-tolerant quantum algorithms for estimating ground-state energies of quantum systems. However, the rapid onset of ill-conditioning might make accurate energies…
We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
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…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on…
In a wide variety of applications including online advertising, contractual hiring, and wireless scheduling, the controller is constrained by a stringent budget constraint on the available resources, which are consumed in a random amount by…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
People employ the function-on-function regression to model the relationship between two random curves. Fitting this model, widely used strategies include algorithms falling into the framework of functional partial least squares (typically…
An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…
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…
High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…