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

We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(105 ). We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel Xeon processors illustrate the benefits of our approach. Key words: generalized algebraic Riccati equation, Newton's method, generalized Lyapunov equation, LR-ADI iteration, parallel algorithms.

• Type: Conference
• Year: 2006
• Where: EUROPAR
• Authors: José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí
• Keywords: Algebraic Riccati Equation, Distributed And Parallel Computing, EUROPAR 2006, Lyapunov Equation, Parallel Algorithms