Related papers: A Preconditioner based on Non-uniform Row Sampling…
We provide an exact analysis of a class of randomized algorithms for solving overdetermined least-squares problems. We consider first-order methods, where the gradients are pre-conditioned by an approximation of the Hessian, based on a…
This paper introduces the Nystr\"om PCG algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nystr\"om method to form a low-rank approximation of the matrix, which leads to an efficient…
In this paper, we investigate the random subsampling method for tensor least squares problem with respect to the popular t-product. From the optimization perspective, we present the error bounds in the sense of probability for the residual…
In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…
For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower precision. These include symmetrically preconditioned normal…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational…
Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully parameterized networks. In this paper, RaNNs are integrated…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
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,…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
We consider approximation algorithms for the problem of finding $x$ of minimal norm $\|x\|$ satisfying a linear system $\mathbf{A} x = \mathbf{b}$, where the norm $\|\cdot \|$ is arbitrary and generally non-Euclidean. We show a simple…
The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…
We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block updates in the solution, and a dynamic proposal distribution…
Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy solutions to least-squares…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such…