Solving the Algebraic Riccati Equation with the Matrix Sign Function
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چکیده
This paper presents solne inrprovements to the matrix-sigll-fllnction algorithn~ for the alge\,raic Riccati equation. A simple reorganization changes nonsynnnetric watrix inversion5 into syinmetric niatrix inversions. Scaling accelerates convergence of the basic iteration ant1 yields a new qnadratic formula for certain 2-by-2 algebraic Riccati eqnation5. Numerical experience suggests the algorithm he supplemented with a refinenwiit strategy similar to iterative refinement for systems of linear equations. Rrfilwllwnt also produces an error estilnate. The resnlting procedure is nulnerically stable. It canpares favorably with current Schur vector-based algoritlnns.
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