Related papers: Randomized Block Krylov Methods for Stronger and F…
Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…
The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
Most current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional…
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…
An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
Low-rank approximation is a task of critical importance in modern science, engineering, and statistics. Many low-rank approximation algorithms, such as the randomized singular value decomposition (RSVD), project their input matrix into a…
Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular…
In recent years two Krylov subspace methods have been proposed for solving skew symmetric linear systems, one based on the minimum residual condition, the other on the Galerkin condition. We give new, algorithm-independent proofs that in…
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 study the general approach to accelerating the convergence of the most widely used solution method of Markov decision processes with the total expected discounted reward. Inspired by the monotone behavior of the contraction mappings in…
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior…
Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…
We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…
Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…
Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the smallest singular values of a tall-skinny matrix. We analyze…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…