This contains some code that implements several algorithms to solve quadratic vector equations from my papers.
A quadratic vector equation is an equation of the form
$$
Mx = a + b(x \otimes x),
$$
where
The main case we are interested in is the one in which
Algorithms depth
, order
, thicknesses
and qve_newton
are from [EP]. These are guaranteed to converge to the minimal nonnegative solution, under the hypotheses in [QVE].
Algorithm perron_iteration
is from [P], and algorithm perron_newton
is from [PN]. These two algorithms assume that
[QVE]: Quadratic vector equations (Federico Poloni), In Linear Algebra and its Applications, volume 438, 2013.
[P]: A Perron iteration for the solution of a quadratic vector equation arising in Markovian binary trees (Beatrice Meini, Federico Poloni), In SIAM J. Matrix Anal. Appl., volume 32, 2011.
[PN]: On the solution of a quadratic vector equation arising in Markovian binary trees (Dario A. Bini, Beatrice Meini, Federico Poloni), In Numer. Linear Algebra Appl., volume 18, 2011.
[EP]: S. Hautphenne, G. Latouche, and M.-A. Remiche. Algorithmic approach to the extinction probability of branching processes. Methodology and Computing in Applied Probability, 2011, 13(1):171-192.
PDFs of my papers can be obtained free of charge at http://pages.di.unipi.it/fpoloni/publications/publications.php.
Feel free to use this code in your research. Just remember cite me if it is appropriate. I mean in your paper, not "summon me in court". Which reminds me: there is no warranty for this program, it's provided "as is", we are not liable for damage, and all that kind of stuff you read in licenses.