Randomized Extended Kaczmarz for Solving Least-Squares
Numerical Analysis
2018-07-24 v3 Data Structures and Algorithms
Abstract
We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by Strohmer and Vershynin.
Cite
@article{arxiv.1205.5770,
title = {Randomized Extended Kaczmarz for Solving Least-Squares},
author = {Anastasios Zouzias and Nikolaos Freris},
journal= {arXiv preprint arXiv:1205.5770},
year = {2018}
}
Comments
19 Pages, 5 figures; code is available at https://github.com/zouzias/REK