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

We consider the iterative solutions of a certain class of algebraic ma trix 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 les s than or equal to 1). Here c denotes the fraction of scattering per c ollision and alpha is an angular shift. Equations of this class are in duced via invariant imbedding and the shifted Gauss-Lengendre quadratu re formula from a ''simple transport model.'' The purpose of this pape r is to describe the effects of the parameters c, alpha, and N (the di mension of the matrix) on the convergence rates of the iterative solut ions. We also compare the convergence rates of those iterative methods .