Research Initiation Award: Numerical Solution of Large-Scale Algebraic Riccati Equations

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The development of parallel and vector algorithms for solving very large matrix algebraic Riccati equations is proposed. The approach to be used stresses the use of computational kernels such as the BLAS3, which are available on a wide variety of parallel computers. This approach will make the algorithms portable to many advanced scientific computers. Much of the research is based on the matrix sign function algorithm, an iterative method that has been shown to work well on a certain class of multiprocessor. Topics for research include easily parallelized "multiplication rich" algorithms, parallel and vector algorithms for several different advanced computer architectures, a condition estimate computable using the matrix sign function, and iterative algorithms for solving the linear Lyapunov equation. Finally, implementation of the algorithms as high quality, reliable mathematical software is proposed, in order to make the results of the research available for use by the control systems community. The solution of algebraic Riccati equations is a fundamental computational problem in control engineering and is essential for the application of many modern control techniques.