Solving SLICOT benchmarks for algebraic Riccati equations by modified Newton´s method

Improved algorithms for solving continuous- and discrete-time algebraic Riccati equations using Newton´s method with or without line search are discussed. The basic theory and algorithms, as well as the developed solvers, are briefly presented. The main results of an investigation of the performance of these solvers on examples from the SLICOT benchmark collections are compared with those obtained using the widely-used MATLAB functions care and dare. The numerical results often show significantly improved accuracy, measured in terms of normalized residuals or relative errors (when exact results are known), and greater efficiency. The use of such algorithms is strongly recommended, especially for improving the solutions computed by other solvers.