IEEE Transactions on Automatic Control · 1979 · 1K citations · 23 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsDynamical SystemsEigenvalue ProblemsMatrix ComputationNumerical AlgorithmsNumerical AnalysisNumerical Linear AlgebraNumerical Methods For Differential EquationsDifferential Equation SolversEigenvalue AlgorithmsEigenvalue ComputationLinear System SolversMatrix Equation SolversMatrix FormulationSchur FunctionsSparse Matrix Techniques
In this paper a new algorithm for solving algebraic Riccati equations (both continuous-time and discrete-time versions) is presented. The method studied is a variant of the classical eigenvector approach and uses instead an appropriate set of Schur vectors, thereby gaining substantial numerical advantages. Considerable discussion is devoted to a number of numerical issues. The method is apparently quite numerically stable and performs reliably on systems with dense matrices up to order 100 or so, storage being the main limiting factor.
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The Algebraic Eigenvalue Problem
E. I., J. H. Wilkinson · Mathematics of Computation · 1966 · 5.2K citations
On a Matrix Riccati Equation of Stochastic Control
W.M. Wonham · SIAM Journal on Control · 1968 · 1K citations