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Published in:
2011 | OriginalPaper | Chapter
A Perron vector iteration for QVEs
Author : Federico Poloni
Published in: Algorithms for Quadratic Matrix and Vector Equations
Publisher: Scuola Normale Superiore
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Equation (1), with the additional conditions
3.1.1
$$M = I, a + b\left( {e,e} \right) = e$$
(
i.e.
, the vector
e
is a solution, though not necessarily the minimal one), arises from the study of a class of branching processes known as Markovian binary trees. These processes model a population composed of a number of individuals, each of which may be in a state φ ∈ {1,2, ...,
n
}. The individuals evolve independently and have state-dependent probabilities of reproducing or dying. Here reproducing means that an individual in state
i
splits into two individuals in state
j
and
k
respectively; the probability of this event is represented by the term b
ijk
in the equation, while the probability of an individual in state
i
dying is
a
i
.