# Randomized Extended Kaczmarz for Solving Least Squares

@article{Zouzias2013RandomizedEK,
title={Randomized Extended Kaczmarz for Solving Least Squares},
author={Anastasios Zouzias and Nikolaos M. Freris},
journal={ArXiv},
year={2013},
volume={abs/1205.5770}
}
• Published in
SIAM J. Matrix Analysis…
2013
• Mathematics, Computer Science
• ArXiv
• We present a randomized iterative algorithm that exponentially converges in the mean square to the minimum $\ell_2$-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 squared condition number of the system multiplied by the number of nonzero entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 102 CITATIONS

## Tight upper bounds for the convergence of the randomized extended Kaczmarz and Gauss-Seidel algorithms

• Kui Du
• Mathematics, Computer Science
• Numerical Lin. Alg. with Applic.
• 2019
VIEW 15 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

## Constrained ERM Learning of Canonical Correlation Analysis: A Least Squares Perspective

• Computer Science, Medicine, Mathematics
• Neural Computation
• 2017
VIEW 7 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

## Distributed Algorithms for Computation of Centrality Measures in Complex Networks

• Computer Science, Mathematics, Physics
• IEEE Transactions on Automatic Control
• 2017
VIEW 4 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

## Efficient Parametric and Non-Parametric Estimation for Localization and Mapping in Robotic Networks

VIEW 5 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

## Computational and Statistical Advances in Testing and Learning

VIEW 9 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

## Learning theory of randomized Kaczmarz algorithm

• Mathematics, Computer Science
• J. Mach. Learn. Res.
• 2015
VIEW 4 EXCERPTS
CITES RESULTS, METHODS & BACKGROUND
HIGHLY INFLUENCED

## Randomized Kaczmarz algorithm for inconsistent linear systems: An exact MSE analysis

• Mathematics, Computer Science
• 2015 International Conference on Sampling Theory and Applications (SampTA)
• 2015
VIEW 11 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

## Randomized gossip algorithms for solving Laplacian systems

• Mathematics, Computer Science
• 2015 European Control Conference (ECC)
• 2015
VIEW 11 EXCERPTS
CITES METHODS & BACKGROUND

## An Asynchronous Consensus-Based Algorithm for Estimation From Noisy Relative Measurements

• Mathematics, Computer Science
• IEEE Transactions on Control of Network Systems
• 2014
VIEW 5 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

## Faster Alternatives to the Randomized Extended Kaczmarz Algorithm

VIEW 7 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

2013
2020

### CITATION STATISTICS

• 16 Highly Influenced Citations

• Averaged 16 Citations per year from 2017 through 2019

• 64% Increase in citations per year in 2019 over 2018

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 48 REFERENCES

## Low rank approximation and regression in input sparsity time

• Mathematics, Computer Science
• STOC '13
• 2013

## A Fast Randomized Algorithm for Orthogonal Projection

• Computer Science, Mathematics
• SIAM J. Scientific Computing
• 2011

## Faster least squares approximation

• Computer Science, Mathematics
• Numerische Mathematik
• 2011

## LSRN: A Parallel Iterative Solver for Strongly Over- or Underdetermined Systems

• Computer Science, Mathematics, Medicine
• SIAM J. Scientific Computing
• 2011

## Low rank matrix-valued chernoff bounds and approximate matrix multiplication

• Mathematics, Computer Science
• SODA '11
• 2011

## Sarlòs. Faster Least Squares Approximation

• P. Drineas, M. W. Mahoney, S. Muthukrishnan
• Numer. Math.,
• 2011

## Blendenpik: Supercharging LAPACK's Least-Squares Solver

• Mathematics, Computer Science
• SIAM J. Scientific Computing
• 2010

## Randomized Methods for Linear Constraints: Convergence Rates and Conditioning

• Mathematics, Computer Science
• Math. Oper. Res.
• 2010