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 distrib uted memory. We apply and extend the available theory for Newton's method e ndowed 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 Lyapun ov equation has to be solved. We propose to solve these Lyapunov equations using iterative schemes for computing the matrix sign function. This approa ch can be efficiently implemented on parallel computers using ScaLAPACK. Nu merical experiments on an IBM SP2 multicomputer report on the accuracy, sca lability, and speed-up of the implemented algorithms. (C) 2000 Elsevier Sci ence B.V. All rights reserved.