RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations
For researchers working on large-scale control and optimization problems, this work provides a unified algorithmic framework, but it is incremental as it shows equivalence rather than new performance gains.
This paper introduces a low-rank ADI-type algorithm for solving large-scale continuous-time algebraic Riccati equations, demonstrating that it produces identical iterates to three previously known methods when using the same parameters.
This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm 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 show that there is a very tight relation between the new algorithm 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.