Abstract
In the present paper, we consider large-scale continuous-time differential\nmatrix Riccati equations having low rank right-hand sides. These equations are\ngenerally solved by Backward Differentiation Formula (BDF) or Rosenbrock\nmethods leading to a large scale algebraic Riccati equation which has to be\nsolved for each timestep. We propose a new approach, based on the reduction of\nthe problem dimension prior to integration. We project the initial problem onto\nan extended block Krylov subspace and obtain a low-dimentional differential\nalgebraic Riccati equation. The latter matrix differential problem is then\nsolved by Backward Differentiation Formula (BDF) method and the obtained\nsolution is used to reconstruct an approximate solution of the original\nproblem. We give some theoretical results and a simple expression of the\nresidual allowing the implementation of a stop test in order to limit the\ndimension of the projection space. Some numerical experiments will be given.\n