engleski

A low-rank ADI-type algorithm for large scale algebraic Riccati equations

In this talk, we present a new algorithm (RADI) for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of RADI is in its immediate and efficient low-rank formulation, which is a generalization of the Cholesky-factored variant of the Lyapunov ADI method. We discuss important implementation aspects of the algorithm, such as reducing the use of complex arithmetic and shift selection strategies. We also show that there is a very tight relation between RADI and three other algorithms for CARE previously known in the literature -- all of these seemingly different methods in fact produce exactly the same iterates when used with the same parameters: they are algorithmically different descriptions of the same approximation sequence to the Riccati solution. Finally, in several numerical experiments we demonstrate that the performance of RADI is very competitive with the state-of-the-art algorithms for solving CARE. This is joint work with Peter Benner, Patrick Kürschner, and Jens Saak.

matrix equations ; algebraic Riccati equations ; ADI iteration ; low rank approximation

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