Publication

MATHICSE Technical Report : A low-rank technique for computing the quasi-stationary distribution of subcritical Galton-Watson processes

2019
Working Papers

Abstract

We present a new algorithm for computing the quasi-stationary distribution of subcritical Galton-Watson branching processes. This algorithm is based on a particular discretization of a well-known functional equation that characterizes the quasi-stationary distribution of these processes. We provide a theoretical analysis of the approximate low-rank structure that stems from this discretization, and we extend the procedure to multitype branching processes. We use numerical examples to demonstrate that our algorithm is both more accurate and more efficient than other approaches.

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2019
Working Papers

Abstract

Official source

Related concepts (9)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

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MATHICSE Technical Report : A low-rank technique for computing the quasi-stationary distribution of subcritical Galton-Watson processes

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