Some numerical considerations and Newton's method revisited for solving algebraic Riccati equations

IEEE Transactions on Automatic Control ◽

10.1109/9.76366 ◽

1991 ◽

Vol 36 (5) ◽

pp. 608-616 ◽

Author(s):

L. Dieci

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations

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Initializing Newton's method for discrete-time algebraic Riccati equations using the butterfly SZ algorithm

Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404) ◽

10.1109/cacsd.1999.808626 ◽

2003 ◽

Author(s):

H. Fassbender ◽

P. Benner

Keyword(s):

Discrete Time ◽

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations

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Inexact Newton’s method with inner implicit preconditioning for algebraic Riccati equations

Computational and Applied Mathematics ◽

10.1007/s40314-015-0274-8 ◽

2015 ◽

Vol 36 (2) ◽

pp. 955-969 ◽

Author(s):

Jean-Paul Chehab ◽

Marcos Raydan

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations

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Newton's Method for Discrete Algebraic Riccati Equations when the Closed-Loop Matrix Has Eigenvalues on the Unit Circle

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/s0895479897322999 ◽

1998 ◽

Vol 20 (2) ◽

pp. 279-294 ◽

Author(s):

Chun-Hua Guo

Keyword(s):

Unit Circle ◽

Newton’S Method ◽

Newton's Method ◽

Closed Loop ◽

Riccati Equations ◽

Algebraic Riccati Equations ◽

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Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search

Parallel Computing ◽

10.1016/s0167-8191(00)00012-0 ◽

2000 ◽

Vol 26 (10) ◽

pp. 1345-1368 ◽

Author(s):

Peter Benner ◽

Ralph Byers ◽

Enrique S Quintana-Ortı́ ◽

Gregorio Quintana-Ortı́

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Line Search ◽

Riccati Equations ◽

Parallel Computers ◽

Algebraic Riccati Equations ◽

Exact Line Search

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Numerical Investigation of Newton’s Method for Solving Discrete-time Algebraic Riccati Equations

Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics ◽

10.5220/0006860600760085 ◽

2018 ◽

Author(s):

Vasile Sima ◽

Peter Benner

Keyword(s):

Numerical Investigation ◽

Discrete Time ◽

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations

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Numerical Investigation of Newton’s Method for Solving Discrete-time Algebraic Riccati Equations

Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics ◽

10.5220/0006860600660075 ◽

2018 ◽

Author(s):

Vasile Sima ◽

Peter Benner

Keyword(s):

Numerical Investigation ◽

Discrete Time ◽

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations

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Analysis and modificaton of Newton's method for algebraic Riccati equations

Mathematics of Computation ◽

10.1090/s0025-5718-98-00947-8 ◽

1998 ◽

Vol 67 (223) ◽

pp. 1089-1106 ◽

Author(s):

Chun-Hua Guo ◽

Peter Lancaster

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations

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Computational Experience in Solving Continuous-time Algebraic Riccati Equations using Standard and Modified Newton’s Method

Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics ◽

10.5220/0004482500050016 ◽

2013 ◽

Keyword(s):

Newton’S Method ◽

Continuous Time ◽

Newton's Method ◽

Riccati Equations ◽

Computational Experience ◽

Algebraic Riccati Equations ◽

Modified Newton’S Method

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Solving SLICOT benchmarks for algebraic Riccati equations by modified Newton's method

2013 17th International Conference on System Theory, Control and Computing (ICSTCC) ◽

10.1109/icstcc.2013.6689006 ◽

2013 ◽

Author(s):

Vasile Sima

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Riccati Equations ◽

Algebraic Riccati Equations ◽

Modified Newton’S Method

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Newton’s method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.09.100 ◽

2007 ◽

Vol 188 (1) ◽

pp. 103-115 ◽

Author(s):

Hiroaki Mukaidani

Keyword(s):

Newton’S Method ◽

Newton's Method ◽

Large Scale ◽

Riccati Equations ◽

Large Scale Systems ◽

Algebraic Riccati Equations ◽

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