ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

Contributed talks on Matrix Equations

Tue 14:30–15:00, Auditorium Jean Monnet, Chair: Frank Uhlig
Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations
Davide Palitta (Università di Bologna)
Joint work with Valeria Simoncini (Universita' di Bologna)

In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the overall computational effort. When data are symmetric, we show that the Frobenius norm of the residual matrix can be computed at significantly lower cost than with available methods, without explicitly solving the reduced problem. For certain classes of problems, the new residual norm expression combined with a memory-reducing device make classical Krylov strategies competitive with respect to more recent projection methods. We present several numerical experiments that illustrate the effectiveness of the new implementation for standard and extended Krylov subspace methods.

  1. Palitta, D. and Simoncini, V., Computationally enhanced projection methods for symmetric Sylvester and Lyapunov equations. ArXiv: 1602.05033.