The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations
Lakhlifa Sadek, Hamad Talibi Alaoui
Abstract
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.
Topics & Concepts
Krylov subspaceLanczos resamplingMathematicsLyapunov functionDifferential equationBlock (permutation group theory)Applied mathematicsMatrix (chemical analysis)Backward differentiation formulaLyapunov equationProjection (relational algebra)Mathematical analysisDifferential algebraic equationAlgorithmLinear systemOrdinary differential equationEigenvalues and eigenvectorsNonlinear systemGeometryPhysicsMaterials scienceQuantum mechanicsComposite materialModel Reduction and Neural NetworksMatrix Theory and AlgorithmsMagnetic Properties and Applications