Name
Title | ||
|---|---|---|
Computational Krylov-based methods for large-scale differential Sylvester matrix problems. |
Abstract | ||
|---|---|---|
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first approach is based on the integral expression of the exact solution and a Krylov method for the computation of the exponential of a matrix times a block of vectors. In the second approach, we first project the initial problem onto a block (or extended block) Krylov subspace and get a low-dimensional differential Sylvester matrix equation. The latter problem is then solved by some integration numerical methods such as BDF or Rosenbrock method and the obtained solution is used to build the low rank approximate solution of the original problem. We give some new theoretical results such as a simple expression of the residual norm and upper bounds for the norm of the error. Some numerical experiments are given in order to compare the two approaches. |
Year | Venue | Field |
|---|---|---|
2018 | Numerical Linear Algebra With Applications | Krylov subspace,Mathematical optimization,Sylvester equation,Generalized minimal residual method,Mathematical analysis,Matrix (mathematics),Sylvester's law of inertia,Sylvester matrix,Numerical analysis,Matrix exponential,Mathematics |
DocType | Volume | Issue |
Journal | 25 | 5 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Hached | 1 | 2 | 2.10 |
| Khalide Jbilou | 2 | 38 | 12.08 |