arXiv subjects

Peter Lancaster

Publications and source records attributed to Peter Lancaster.

3 recordsLinked to original sources

arXiv2017

Inverse Spectral Problems for Linked Vibrating Systems and Structured Matrix Polynomials

We show that for a given set $\Lambda$ of $nk$ distinct real numbers $\lambda_1, \lambda_2, \ldots, \lambda_{nk}$ and $k$ graphs on $n$ nodes, $G_0, G_1,\ldots,G_{k-1}$, there are real symmetric $n\times n$ matrices $A_s$, $s=0,1,\ldots, k$, such that the matrix polynomial $A(z) := A_k z^k + \cdots + A_1 z + A_0$ has $\Lambda$ as its spectrum, the graph of $A_s$ is $G_s$ for $s=0,1,\ldots,k-1$, and $A_k$ is an arbitrary positive definite diagonal matrix. When $k=2$, this solves a physically significant inverse eigenvalue problem for linked vibrating systems (see Corollary 5.3).

math.SP↗

arXiv2007

On the boundary of the pseudospectrum and its fault points

The theme of this paper was motivated by the question: How effective are path-following procedures for tracing the pseudospectral boundary? The present study of the mathematical properties of the boundary of the pseudospectrum is the result. This boundary is generally made up piecewise smooth curves. We shown how the Schur triangular form of the matrix can be used to analyse dynamical properties of the singular points on these curves.

math.SP↗

arXiv2006

On Pseudospectra of Matrix Polynomials and their Boundaries

In the first part of this paper, the main concern is with smoothness properties of the boundary of the pseudospectrum of a matrix polynomial. In the second part, results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the proximity to such polynomials.

math.SP↗