Parallel Solution of Large Lyapunov Equations

Abstract

In this paper two algorithms for the solution of large-order $(100 \leq n \leq 1000)$ Lyapunov equations $AX + XA^T + Q = 0$ are presented. First, a parallel version of the Hammarling algorithm for the solution of Lyapunov equations where the coefficient matrix A is large and dense is presented. Then a novel iterative parallel algorithm, called full-rank perturbed iteration (FRPI), is presented for the solution of Lyapunov equations where the matrix A is large and banded.