CONVERGENCE-RATES OF ITERATIVE SOLUTIONS OF ALGEBRAIC MATRIX RICCATI-EQUATIONS

We consider the iterative solutions of a certain class of algebraic matrix Riccati equations with two parameters, c(0 less than or equal to c less than or equal to 1) and alpha(0 less than or equal to alpha less than or equal to 1). Here c denotes the fraction of scattering per collision and alpha 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 parameters c, alpha, and N (the dimension of the matrix) on the convergence rates of the iterative solutions. We also compare the convergence rates of those iterative methods.