The eigenvectors of a symmetric matrix can be chosen to form a biorthogonal set with respect to the identity and to the matrix itself. Similarly, the eigenvectors of a symmetric de nite linear pencil can be chosen to be biorthogonal with respect to the pair.This paper presents the three sets of matrix weights, with respect to which the eigenvectors of the symmetric de nite quadratic pencil are ...

This paper is devoted to the study of perturbations a matrix pencil, structured or unstructured, such that perturbed pencil will reproduce given deflating pair while maintaining invariance complementary pair. If latter unknown, it referred as no spillover updating. The specific structures considered in this include symmetric, Hermitian, ?-even, ?-odd and ?-skew-Hamiltonian/Hamiltonian pencils. ...

This paper proposes a new parameter estimation algorithm for damped sinusoidal signals. Parameter estimation for damped sinusoidal signals with additive white noise is a problem of signiicant interest in many signal processing applications, like analysis of NMR data and system identiication. The new algorithm estimates the signal parameters using a matrix pencil constructed from the measured da...

The algorithm of construction of solutions of the unilateral quadratic matrix equation in case of complex eigenvalues of the corresponding matrix pencil is offered. As application, the problem of updating parameters of model by experimentally estimation of eigenvalues of this system is considered. Efficiency of the offered procedure of updating is shown on the example of system with two degree ...

Convolution/superposition software has been used to produce a library of photon pencil beam dose matrices. This library of pencil beams is designed to serve as a tool for both education and investigation in the field of radiotherapy optimization. The elegance of this pencil beam model stems from its cylindrical symmetry. Because of the symmetry, the dose distribution for a pencil beam from any ...