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Regularization Kaczmarz Tools Version 1.4 for Matlab

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Be the first to rate this file! 6 Downloads (last 30 days) File Size: 127 KB File ID: #43791 Version: 1.4.1
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Regularization Kaczmarz Tools Version 1.4 for Matlab

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07 Oct 2013 (Updated )

Implementation of algorithms based on Kaczmarz method for various linear systems

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Description

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.

http://www.math.nthu.edu.tw/~amen/2013/1302252(final).pdf

Acknowledgements

Regtools inspired this file.

Required Products MATLAB
MATLAB release MATLAB 7.13 (R2011b)
MATLAB Search Path
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Other requirements Dependency: http://www.mathworks.com/matlabcentral/fileexchange/52-regtools http://www2.imm.dtu.dk/~pcha/AIRtools/
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Updates
08 Oct 2013 1.1

Title changing.

22 Jan 2014 1.2

Added a link to the main article.

20 Oct 2014 1.3

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

15 Aug 2015 1.4

Changes: summary, and description. Added new algorithms.

15 Aug 2015 1.4.1

Minor updates

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