Convergence rates of iterative solutions of algebraic matrix Riccati equations

摘要

We consider the iterative solutions of a certain class of algebraic matrix Riccati equations with two parameters,c(0 ɤ c ɤ 1) andα(0 ≤ α ≤1). Herec denotes the fraction of scattering per collision and α is an angular shift. Equations of this class are induced via invariant imbedding and the shifted Gauss-Lengendre quadrature formula from a “simple transport model.”The purpose of this paper is to describe the effects of the parametersc, α, andN (the dimension of the matrix) on the convergence rates of the iterative solutions. We also compare the convergence rates of those iterative methods.