Block variants of Hammarling's method for solving Lyapunov equations

Authors:
Daniel Kressner
Affiliations:
Umeå University, Umeå, Sweden
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2008

Citing 17
Cited 1

A set of level 3 basic linear algebra subprograms

ACM Transactions on Mathematical Software (TOMS)
A note on Hammarling's algorithm for the discrete Lyapunov equation

Systems & Control Letters
Numerical solution of the discrete-time, convergent, non-negative definite Lyapunov equation

Systems & Control Letters
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Applied numerical linear algebra

Applied numerical linear algebra
Parallel Wavefront Algorithms Solving Lyapunov Equations for the Cholesky Factor on Message Passing Multiprocessors

The Journal of Supercomputing
LAPACK Users' guide (third ed.)

LAPACK Users' guide (third ed.)
Solution of the matrix equation AX + XB = C [F4]

Communications of the ACM
The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance

SIAM Journal on Matrix Analysis and Applications
The Multishift QR Algorithm. Part II: Aggressive Early Deflation

SIAM Journal on Matrix Analysis and Applications
Recursive blocked algorithms for solving triangular systems—Part I: one-sided and coupled Sylvester-type matrix equations

ACM Transactions on Mathematical Software (TOMS)
Recursive blocked algorithms for solving triangular systems—Part II: two-sided and generalized Sylvester and Lyapunov matrix equations

ACM Transactions on Mathematical Software (TOMS)
Parallel Cyclic Wavefront Algorithms for Solving Semidefinite Lyapunov Equations

Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Formal derivation of algorithms: The triangular sylvester equation

ACM Transactions on Mathematical Software (TOMS)
Low-Rank Solution of Lyapunov Equations

SIAM Review
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)

Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Improving the performance of reduction to Hessenberg form

ACM Transactions on Mathematical Software (TOMS)

Parallel Solvers for Sylvester-Type Matrix Equations with Applications in Condition Estimation, Part I: Theory and Algorithms

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

This article is concerned with the efficient numerical solution of the Lyapunov equation AT X + XA &equls; −C with a stable matrix A and a symmetric positive semidefinite matrix C of possibly small rank. We discuss the efficient implementation of Hammarling's method and propose among other algorithmic improvements a block variant, which is demonstrated to perform significantly better than existing implementations. An extension to the discrete-time Lyapunov equation ATXA − X = −C is also described.