Krylov subspace methods have proved effective for many non-Hermitian eigenvalue problems, yet the analysis of such algorithms is involved. Convergence can be characterized by the angle the approximating subspace forms with a desired invariant subspace, resulting in a geometric framework that is robust to eigenvalue ill-conditioning. This paper describes a new bound on this angle that handles th...

Suppose one approximates an invariant subspace of an n n matrix in C nn which in not necessarily self{adjoint. Suppose that one also has an approximation for the corresponding eigenvalues. We consider the question of how good the approximations are. Speciically, we develop bounds on the angle between the approximating subspace and the invariant subspace itself. These bounds are functions of the...

In this paper, we describe some recent developments in the use of projection methods to produce reduced-order models for linear time-invariant dynamic systems. Previous related eeorts in model reduction problems from various applications are also discussed. An overview is given of the theory governing the deenition of the family of Rational Krylov methods, the practical heuristics involved and ...

sl(2)−Quasi-Exactly-Solvable (QES) generalization of the rationalAn, BCn, G2, F4, E6,7,8 Olshanetsky-Perelomov Hamiltonians including many-body Calogero Hamiltonian is found. This generalization has a form of anharmonic perturbations and it appears naturally when the original rational Hamiltonian is written in a certain Weyl-invariant polynomial variables. It is demonstrated that for the QES Ha...

In this paper we discuss the stabilization of large scale linear time invariant dynamical systems via feedback. Efficient schemes based on the Discrete Riccati Difference Equation are presented. The SQR variant is described in detail and a more efficient version, CSQR, is motivated. 1 The Problem In this paper, we focus on the stabilization of a discrete-time system (1) where and are and real m...

Given a nilpotent endomorphism, we consider the manifold of invariant subspaces having a fixed Segre characteristic. In [Linear Algebra Appl., 332–334 (2001) 569], the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces is obtained. Here we obtain the explicit form of this deformation when the invariant subspace is ...

0. Introduction. Let H be a complex Hilbert space of finite or infinite dimension, and let E be a collection of bounded linear operators on H. We say E is reducible if there exists a subspace of H, closed by definition and different from the trivial subspaces {0} and H which is invariant under every member of E . We call E triangularizable if the set of invariant subspaces under E contains a ma...

An operator is uniform if its restriction to any infinite-dimensional invariant subspace is unitarily equivalent to itself. We show that a uniform operator having a proper infinite-dimensional invariant subspace resembles an analytic Toeplitz operator in the way that the weakly closed algebra generated by it and the identity operator is isomorphic to a subalgebra of the Calkin algebra; furtherm...

Abstract: By using the concept of parameter varying (C,A)-invariant subspace and parameter varying unobservability subspace, this paper investigates the problem of fault detection and isolation in linear parameter varying (LPV) systems. The so called detection filters approach, formulated as the fundamental problem of residual generation (FPRG) for linear time invariant (LTI) systems is extende...