An inverse-free ADI algorithm for computing Lagrangian invariant subspaces
نویسندگان
چکیده
منابع مشابه
An inverse-free ADI algorithm for computing Lagrangian invariant subspaces
The numerical computation of Lagrangian invariant subspaces of large scale Hamiltonian matrices is discussed in the context of the solution of Lyapunov and Riccati equations. A new version of the low-rank alternating direction implicit method is introduced, which in order to avoid numerical difficulties with solutions that are of very large norm, uses an inverse-free representation of the subsp...
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The computation of Lagrangian invariant subspaces of a Hamiltonian matrix, or the closely related task of solving algebraic Riccati equations, is an important issue in linear optimal control, stochastic control and H∞-design. We propose a new class of Riemannian Newton methods that allows to compute isolated Lagrangian invariant subspaces of a Hamiltonian matrix. The algorithm implements a vari...
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[13] V. Mehrmann, A Symplectic orthogonal method for single input or single output discrete time optimal control problems, in Linear Algebra in Signals Systems and Control, B. N. Datta et al eds. SIAM Philadelphia, Penn. pp.128-140(1988). [14] K. C. Ng and B. N. Parlett, Development of an accurate algorithm for EXP(Bt), Part I, Programs to swap diagonal block, Part II, CPAM-294, University of C...
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ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2015
ISSN: 1070-5325
DOI: 10.1002/nla.2018