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The JSR toolbox

version 1.21 (321 KB) by Raphael Jungers
Gathers and compares the best methods for the joint spectral radius computation


Updated 22 Mar 2016

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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

Cite As

Raphael Jungers (2020). The JSR toolbox (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)


In jointTriangul, the return value for block in the 1d case should be {M}, instead of M, in order to have the same output format as for the higher-dimensional case, i.e.

if n==1
B = 1;

Antonio Cicone



Fixed the 1D bug

Fixed a bug: now treats as a special case the one-by-one matrices.

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

Technical update for some minor modifications

Set version to 1.1

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

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

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

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.

two overflow bugs fixed (in jsr_prod_Gripenberg and jsr_prod_pruning_Algorithm)

typos/references corrected

readme updated: please use sedumi version 1.3

contact address

contact address updated

email contact address:

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired: The CSSystem toolbox