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  4. The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations

The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations

MMC.
2021;
Volume 8, Number 3
: pp. 526–536
https://doi.org/10.23939/mmc2021.03.526
Received: December 24, 2020
Accepted: August 15, 2021

Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 526–536 (2021)

Authors:
  1. L. Sadek
  2. H. Talibi Alaoui
1
Department of Mathematics, Faculty of Science, Chouaib Doukkali University
2
Department of Mathematics, Faculty of Science, Chouaib Doukkali University

In this paper, we present a new approach for solving large-scale differential Lyapunov equations.  The proposed approach is based on projection of the initial problem onto an extended block Krylov subspace by using  extended nonsymmetric block Lanczos algorithm then, we get a low-dimensional differential Lyapunov matrix equation.  The latter differential matrix equation is solved by the Backward Differentiation Formula method (BDF) or Rosenbrock method (ROS), the obtained solution allows to build a low-rank approximate solution of the original problem.  Moreover, we also give some theoretical results.  The numerical results demonstrate the performance of our approach.

extended block Krylov subspace
extended nonsymmetric block Lanczos algorithm
low-rank approximation
differential Lyapunov equations
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