This paper presents algorithms for computing stable Lagrangian invariant subspaces of a Hamiltonian matrix and a symplectic pencil, respectively, having purely imaginary and unimodular eigenvalues. The problems often arise in solving continuousor discrete-time H∞-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to determine an isotropic...

The Rational Krylov Sequence (RKS) method can be seen as a generalisation of Arnoldi's method. It projects a matrix pencil onto a smaller subspace; this projection results in a small upper Hessenberg pencil. As for the Arnoldi method, RKS can be restarted implicitly, using the QR decomposition of a Hessenberg matrix. This restart comes with a projection of the subspace using a rational function...

Wireless ad-hoc sensor networks (WASN) are attracting research interest recently because of their various applications in distributed monitoring, communication, and computing. In this paper, we concentrate on the range error problem of WASN positioning algorithms. A new matrix pencil based time of arrival (TOA) positioning method (MPP) is proposed for WASN. The new scheme employs matrix pencil ...

We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary...

We propose a computationally efficient and numerically reliable algorithm to compute Kronecker-like forms of periodic matrix pairs. The eigenvalues and Kronecker indices are defined via the Kro-necker structure of an associated lifted matrix pencil. The proposed reduction method relies on structure preserving manipulations of this pencil to extract successively lower complexity subpencils which...

This paper extends the low complexity, Matrix Pencil direction of arrival (DOA) estimation algorithm to the CDMA case. The CDMA processing gain is used to suppress interfering signals, allowing Matrix Pencil to accurately estimate the DOA of the signal of interest. It is shown here that this CDMA/MP algorithm is able to estimate an angle of arrival (AOA) with a low mean square error using only ...