Related papers: Preconditioning Kaczmarz method by sketching
We propose a preconditioner that can accelerate the rate of convergence of the Multiple Shooting Shadowing (MSS) method. This recently proposed method can be used to compute derivatives of time-averaged objectives (also known as…
The Kaczmarz algorithm is an iterative method for solving a system of linear equations. It can be extended so as to reconstruct a vector $x$ in a (separable) Hilbert space from the inner-products $\{\langle x, \phi_{n} \rangle\}$. The…
Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure…
We present new adaptive sampling rules for the sketch-and-project method for solving linear systems. To deduce our new sampling rules, we first show how the progress of one step of the sketch-and-project method depends directly on a…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…
Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…
CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a randomized preconditioner framework for CholeskyQR algorithm.…
Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability is limited when dealing with inconsistent systems or…
The Sampling Kaczmarz Motzkin (SKM) algorithm is a generalized method for solving large scale linear systems of inequalities. Having its root in the relaxation method of Agmon, Schoenberg, and Motzkin and the randomized Kaczmarz method, SKM…
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…
Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. Proposed M-IHS techniques are obtained by incorporating the Heavy…
Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$. One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
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…
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…