An Exact Line Search method for solving generalized continuous-time algebraic Riccati equations

We present a Newton-like method for solving algebraic Riccati equations that uses Exact Line Search to improve the sometimes erratic convergence behavior of Newton's method. It avoids the problem of a disastrously large first step and accelerates convergence when Newton steps are too small or too long, The additional work to perform the Line search is small relative to the work needed to calculate the Newton step.