Related papers: Optimal Krylov On Average
This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
Randomized sketching is currently introduced into every area of numerical linear algebra. In Krylov subspace methods, it allows runtime savings at the cost of small accuracy reductions. This work offers a different view on sketching in…
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…
Many large-scale stochastic optimization algorithms involve repeated solutions of linear systems or evaluations of log-determinants. In these regimes, computing exact solutions is often unnecessary; it is more computationally efficient to…
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…
Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without spending computational effort on a dual problem. Estimates…
A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…
We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…
We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random…
This paper presents an efficient algorithm to solve total variation (TV) regularizations of images contaminated by a both blur and noise. The unconstrained structure of the problem suggests that one can solve a constrained optimization…
We set up, at the abstract Hilbert space setting, the general question on when an inverse linear problem induced by an operator of Friedrichs type admits solutions belonging to (the closure of) the Krylov subspace associated to such…
The Krylov subspace method is a standard approach to approximate quantum evolution, allowing to treat systems with large Hilbert spaces. Although its application is general, and suitable for many-body systems, estimation of the committed…
Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development of these methods. In this work, we develop Krylov subspace…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…