Related papers: Where Have All the Kaczmarz Iterates Gone?
A class of fast greedy block Kaczmarz methods combined with general greedy strategy and average technique are proposed for solving large consistent linear systems. Theoretical analysis of the convergence of the proposed method is given in…
We prove that for linear, discrete, time-varying, deterministic system (perfect model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance…
The Kaczmarz method for solving a linear system $Ax = b$ interprets such a system as a collection of equations $\left\langle a_i, x\right\rangle = b_i$, where $a_i$ is the $i-$th row of $A$, then picks such an equation and corrects $x_{k+1}…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
The block Kaczmarz method and its variants are designed for solving the over-determined linear system. They involve iteratively projecting the current point onto the solution space of a subset of constraints. In this work, by alternately…
In this technical report we present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of the phase retrieval problem via substituting at each…
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…
We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the…
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…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
This paper studies the robustness of policy iteration in the context of continuous-time infinite-horizon linear quadratic regulation (LQR) problem. It is shown that Kleinman's policy iteration algorithm is inherently robust to small…
The sampling Kaczmarz-Motzkin (SKM) method is a generalization of the randomized Kaczmarz and Motzkin methods. It first samples some rows of coefficient matrix randomly to build a set and then makes use of the maximum violation criterion…
A new algorithm called accelerated projection-based consensus (APC) has recently emerged as a promising approach to solve large-scale systems of linear equations in a distributed fashion. The algorithm adopts the federated architecture, and…
Neural network constraint satisfaction is crucial for safety-critical applications such as power system optimization, robotic path planning, and autonomous driving. However, existing constraint satisfaction methods face…
In this paper, the zero-forcing and regularized zero-forcing schemes operating in crowded extra-large MIMO (XL-MIMO) scenarios with a fixed number of subarrays have been emulated using the randomized Kaczmarz algorithm (rKA). For that,…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…