The matrix sign function and computations in systems
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Publication:1254088
DOI10.1016/0096-3003(76)90020-5zbMath0398.65023OpenAlexW1985242550WikidataQ56545206 ScholiaQ56545206MaRDI QIDQ1254088
Eugene D. Denman, Alex N. jun. Beavers
Publication date: 1976
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0096-3003(76)90020-5
ExamplesAlgebraic Eigenvalue-Eigenvector ProblemAlgebraic Matrix Riccati EquationsCoupled Riccati EquationsLyapunov EquationsMatrix Sign FunctionMatrix Square RootsNew AlgorithmsPole AssignmentSpectral Factorization
Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Algorithms in computer science (68W99)
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Cites Work
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- A new similarity transformation method for eigenvalues and eigenvectors
- On the matrix Riccati equation
- Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
- A Computational Algorithm for Solving a System of Coupled Algebraic Matrix Riccati Equations
- Optimization of multiple-input systems with assigned poles
- An Additional Algorithm for a System of Coupled Algebraic Matrix Riccati Equations
- Matrix Quadratic Solutions
- Some Applications of the Lyapunov Matrix Equation
- Design of optimal control systems with prescribed eigenvalues†