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

We investigate the numerical solution of continuous-time algebraic Riccati equations via Newton's method on serial and parallel computers with distributed memory. We apply and extend the available theory for Newton's method endowed with exact line search to accelerate convergence. We also...

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Bibliographic Details
Published in:Parallel computing 2000-09, Vol.26 (10), p.1345-1368
Main Authors: Benner, Peter, Byers, Ralph, Quintana-Ortı́, Enrique S, Quintana-Ortı́, Gregorio
Format: Article
Language:English
Subjects:
Continuous-time algebraic Riccati equation
Line search
Lyapunov equation
Matrix sign function
Newton's method
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Summary:We investigate the numerical solution of continuous-time algebraic Riccati equations via Newton's method on serial and parallel computers with distributed memory. We apply and extend the available theory for Newton's method endowed with exact line search to accelerate convergence. We also discuss a new stopping criterion based on recent observations regarding condition and error estimates. In each iteration step of Newton's method a stable Lyapunov equation has to be solved. We propose to solve these Lyapunov equations using iterative schemes for computing the matrix sign function. This approach can be efficiently implemented on parallel computers using ScaLAPACK. Numerical experiments on an ibm sp2 multicomputer report on the accuracy, scalability, and speed-up of the implemented algorithms.
ISSN:0167-8191
1872-7336
DOI:10.1016/S0167-8191(00)00012-0