Regularization Kaczmarz Tools Version 1.4 for Matlab

Implementation of algorithms based on Kaczmarz method for various linear systems
Updated 15 Aug 2015

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The new version 1.4 includes the original implementations of Block Kaczmarz Algorithm:
* Block Kaczmarz Algorthm based on solving linear systems with arrowhead matrices. Cyclic Control.
* Same as above, but with randomized control scheme for two distribution.
* Direct Projection Method (DPM).
Pending for publishing: July 2015.
For earlier versions (<1.4):
This library contains four new modifications of the algorithm S. Kaczmarz:
* Quasi-optimal Kaczmarz method
* Column Kaczmarz method for Tikhonov regularization problem
* Column Kaczmarz method with quasi-optimal rule for Tikhonov regularization problem
* Randomized Column Kaczmarz method for Tikhonov regularization problem
In this files, we consider Phillips's "famous" test problem. This new algorithms is based on transforming regularized normal equations to the equivalent augmented regularized normal system of equations.

Main article: Ivanov A.A., Zhdanov A.I. Kaczmarz algorithm for Tikhonov regularization problem, Appl. Math. E-Notes, 13(2013), pp. 270-276.

Cite As

Andrey Ivanov (2024). Regularization Kaczmarz Tools Version 1.4 for Matlab (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2011b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes

Minor updates

Changes: summary, and description. Added new algorithms.

Added two new methods and updated examples. Increased to 1.1 version.

Added a link to the main article.

Title changing.