Computing the Least Fixed Point of Positive Polynomial Systems

We consider equation systems of the form X1 = f1(X1, . . . , Xn), . . . , Xn = fn(X1, . . . , Xn) where f1, . . . , fn are polynomials with positive real coefficients. In vector form we denote such an equation system by X = f(X) and call f a system of positive polynomials, short SPP. Equation systems of this kind appear naturally in the analysis of stochastic models like stochastic context-free grammars (with numerous applications to natural language processing and computational biology), probabilistic programs with procedures, web-surfing models with back buttons, and branching processes. The least nonnegative solution

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Javier Esparza, Stefan Kiefer, Michael Luttenberger
• Keywords: CORR 2010, Education, Equation Systems, Positive Real Coefficients, Spp Equations