Computational Experience with a Modified Newton Solver for Discrete-Time Algebraic Riccati Equations

Improved Newton solvers, with or without line search, for continuous-time algebraic Riccati equations are discussed. The basic theory and algorithms are briefly presented. Algorithmic details, the computational steps, and convergence tests are described. The main results of an extensive performance investigation of the Newton solvers are compared with those obtained using the widely-used MATLAB solver, care. Randomly generated systems with orders till 2,000, as well as the systems from the large COMPl\(_e\)ib collection of examples, are considered. Significantly improved accuracy, in terms of normalized and relative residuals, and often greater efficiency than for care have been obtained. The results strongly recommend the use of such algorithms, especially for improving the solutions computed by other solvers.

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