A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation
A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation
A special instance of the algebraic Riccati equation $XCX-XE-AX+B=0$ where the $n\times n$ matrix coefficients $A,B,C,E$ are rank structured matrices is considered. Relying on the structural properties of Cauchy-like matrices, an algorithm is designed for performing the customary Newton iteration in $O(n^2)$ arithmetic operations (ops). The same technique is used …