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The JSR toolbox

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The JSR toolbox



10 Oct 2011 (Updated )

Gathers and compares the best methods for the joint spectral radius computation

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The Joint Spectral Radius of a set of matrices characterizes the maximal asymptotic rate of growth of a product of matrices taken in this set, when the
length of the product increases.
It is known to be very hard to compute. In recent years, many different methods have been proposed to approximate it.
These methods have different advantages, depending on the application considered, the type of matrices considered, the desired accuracy or running time, etc.
The goal of this toolbox is to provide the practioner with the best available methods, and propose an easy tool for the researcher to compare the different methods.
This is version 1.2. Please report any bug, comment or suggestion to


This file inspired The Cs System Toolbox.

MATLAB release MATLAB 7.12 (R2011a)
MATLAB Search Path
Other requirements A semi-definite solver is required for some methods.
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Comments and Ratings (1)
25 Oct 2011 Antonio Cicone  
12 Oct 2011 1.1

email contact address:

12 Oct 2011 1.2

contact address updated

17 Oct 2011 1.3

contact address

18 Oct 2011 1.5

readme updated: please use sedumi version 1.3

18 Oct 2011 1.6

typos/references corrected

24 Oct 2011 1.7

two overflow bugs fixed (in jsr_prod_Gripenberg and jsr_prod_pruning_Algorithm)

23 Oct 2013 1.11

We have fixed a few minor bugs, updated methods according to the recent literature (in particular jsr.m),

improved usability, and added a benchmark. See ChangeLog.txt for an exhaustive list.

24 Oct 2013 1.14

Replaced two methods under GNU license by genuine ones (vec.m and mat.m).

05 Feb 2014 1.15

Bug fixed, see changelog.txt.
Added a pdf article on the toolbox.

12 Sep 2014 1.16

Addition: Method jsr_pathcomplete.m and some useful subroutines

Change : Some functions use the interface solve_semi_definite_program instead of calling directly SeDuMi

Fix : memory bug in jsr_lift_semidefinite.m

12 Sep 2014 1.17

Set version to 1.1

12 Sep 2014 1.18

Technical update for some minor modifications

18 Aug 2015 1.19

We fixed some bugs related to sets of matrices with a spectral radius equal to zero.
Also, we added a new method deciding if a set of matrices has a zero-jsr.
More details in the file changelogs.txt

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