Computational Experience in Solving Continuous-time Algebraic Riccati Equations using Standard and Modified Newton's Method

摘要

Improved algorithms for solving continuous-time algebraic Riccati equations using Newton's method with or without line search are discussed. The basic theory and Newton's algorithms are briefly presented. Algorithmic details the developed solvers are based on, the main computational steps (finding the Newton direction, finding the Newton step size), and convergence tests are described. The main results of an extensive performance investigation of the solvers based on Newton's method are compared with those obtained using the widely-used MATLAB solver. Randomly generated systems with orders till 2000, as well as the systems from a large collection of examples, are considered. The numerical results often show significantly improved accuracy, measured in terms of normalized and relative residuals, and greater efficiency than the MATLAB solver. The results strongly recommend the use of such algorithms, especially for improving the solutions computed by other solvers.