Related papers: A fast solver for linear systems with displacement…
The random reshuffling Kaczmarz (RRK) method enjoys the simplicity and efficiency in solving linear systems as a Kaczmarz-type method, whereas it also inherits the practical improvements of the stochastic gradient descent (SGD) with random…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
It is shown that if the system of the Euler equations has a special global in time smooth solution with the linear profile of velocity, then another solutions with Cauchy data, close in the Sobolev norm to the initial data of the given…
The low-rank approximation properties of Randomly Pivoted LU (RPLU), a variant of Gaussian elimination where pivots are sampled proportional to the squared entries of the Schur complement, are analyzed. It is shown that the RPLU iterates…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and…
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…
Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
We present a non-iterative solver based on the Schur complement method for sparse linear systems of special form which appear in Quantum Monte-Carlo (QMC) simulations of strongly interacting fermions on the lattice. While the number of…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $\mathbb{R}^d$ with respect to the square loss. Our main result is an efficient algorithm for this learning task…
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…
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…
The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert $C^*$-modules and establish analogues of its…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
We present new iterative algorithms for solving a square linear system $Ax=b$ in dimension $n$ by employing the {\it Triangle Algorithm} \cite{kal12}, a fully polynomial-time approximation scheme for testing if the convex hull of a finite…