scholarly journals RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations

2017 ◽  
Vol 138 (2) ◽  
pp. 301-330 ◽  
Author(s):  
Peter Benner ◽  
Zvonimir Bujanović ◽  
Patrick Kürschner ◽  
Jens Saak
Keyword(s):  
Large Scale ◽  
Riccati Equations ◽  
Low Rank ◽  
Algebraic Riccati Equations ◽  
Type Algorithm

scholarly journals An inexact low-rank Newton–ADI method for large-scale algebraic Riccati equations

2016 ◽  
Vol 108 ◽  
pp. 125-142 ◽  
Author(s):  
Peter Benner ◽  
Matthias Heinkenschloss ◽  
Jens Saak ◽  
Heiko K. Weichelt
Keyword(s):  
Large Scale ◽  
Riccati Equations ◽  
Low Rank ◽  
Adi Method ◽  
Algebraic Riccati Equations

scholarly journals Inexact Kleinman-Newton-ADI Method with Line Search to Solve Large-Scale Algebraic Riccati Equations

2015 ◽  
Author(s):  
Heiko K. Weichelt ◽  
Matthias Heinkenschloss ◽  
Jens Saak ◽  
Peter Benner
Keyword(s):  
Newton Method ◽  
Large Scale ◽  
Line Search ◽  
Lyapunov Equation ◽  
Riccati Equations ◽  
Convergence Result ◽  
Low Rank ◽  
Algebraic Riccati Equations ◽  
Newton Step ◽  
The Difference

This poster shows recent improvements of the inexact Kleinman-Newton method for solving algebraic Riccati equations by incorporating a line search and by systematically integrating the low-rank structure resulting from ADI methods for the approximate solution of the Lyapunov equation that needs to be solved to compute the Kleinman-Newton step. A convergence result is pointed out that tailors the convergence proof for general inexact Newton methods to the structure of Riccati equations and avoids positive semi-definiteness assumptions on the difference between certain matrices and the Lyapunov equation residual, which in general do not hold for low-rank approaches. On a test example, the improved inexact Kleinman-Newton method demonstrates its advantages.

Parallel Solution of Large-Scale and Sparse Generalized Algebraic Riccati Equations

2006 ◽  
pp. 710-719 ◽  
Author(s):  
José M. Badía ◽  
Peter Benner ◽  
Rafael Mayo ◽  
Enrique S. Quintana-Ortí
Keyword(s):  
Large Scale ◽  
Riccati Equations ◽  
Parallel Solution ◽  
Algebraic Riccati Equations

scholarly journals A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems

2020 ◽  
Vol 42 (2) ◽  
pp. A957-A996 ◽  
Author(s):  
Peter Benner ◽  
Zvonimir Bujanović ◽  
Patrick Kürschner ◽  
Jens Saak
Keyword(s):  
Continuous Time ◽  
Large Scale ◽  
Riccati Equations ◽  
Numerical Comparison ◽  
Algebraic Riccati Equations

scholarly journals On two numerical methods for the solution of large-scale algebraic Riccati equations

2013 ◽  
Vol 34 (3) ◽  
pp. 904-920 ◽  
Author(s):  
V. Simoncini ◽  
D. B. Szyld ◽  
M. Monsalve
Keyword(s):  
Numerical Methods ◽  
Large Scale ◽  
Riccati Equations ◽  
Algebraic Riccati Equations
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