Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599079 | Linear Algebra and its Applications | 2015 | 17 Pages |
Abstract
The extinction probability of the Markovian Binary Tree (MBT) is the minimal nonnegative solution of a Quadratic Vector Equation (QVE). In this paper, we present a perturbation analysis for the extinction probability of a supercritical MBT. We derive a perturbation bound for the minimal nonnegative solution of the QVE, which is a bound on the difference between the solutions of two nearby equations in terms of the perturbation magnitude. A posteriori error bound is also given, which is a bound on the distance between an approximate solution and the real solution, in terms of the residual of the approximate solution. Numerical experiments show that these bounds are fairly sharp.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pei-Chang Guo, Yun-Feng Cai, Jiang Qian, Shu-Fang Xu,