A modified simple iterative method for nonsymmetric algebraic Riccati equations arising in transport theory
Recently, the algebraic Riccati equation arising in transport theory, \(XCX -XE -AX +B =0\), was shown to be in essence equivalent to a vector equation and a simple but efficient iterative process to compute the minimal positive solution has been presented. Through the process, a sequence of \(\{(u^{(k)}\), \(v^{(k)} )\}\) was computed. In this paper, a modified iterative method is proposed, in which the computation of \(v^{(k)}\) utilizes previously computed \(u^{(k)}\). Numerical results verify the effectiveness of the method.
nonsymmetric algebraic Riccati equations
scientific article; zbMATH DE number 5078439