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- Peter Lancaster
- 2002

We propose a definition for geometric mean of k positive (semi) definite matrices. We show that our definition is the only one in the literature that has the properties that one would expect from a geometric mean, and that our geometric mean generalizes many inequalities satisfied by the geometric mean of two positive semidefinite matrices. We prove some… (More)

- Peter Lancaster, Leiba Rodman
- SIAM Review
- 2005

- PETER LANCASTER
- 2008

This note contains a short review of the notion of linearization of regular matrix polynomials. The objective is clarification of this notion when the polynomial has an " eigenvalue at infinity ". The theory is extended to admit reduction by locally unimodular analytic matrix functions.

- Chun-Hua Guo, Peter Lancaster
- Math. Comput.
- 1999

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X + A * X −1 A = Q and X − A * X −1 A = Q, where Q is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton's method and inversion free variants of the basic fixed point… (More)

- Peter Lancaster, Panayiotis Psarrakos
- SIAM J. Matrix Analysis Applications
- 2005

The pseudospectra of a matrix polynomial P (λ) are sets of complex numbers that are eigenvalues of matrix polynomials which are near to P (λ), i.e., their coefficients are within some fixed magnitude of the coefficients of P (λ). Pseudospectra provide important insights into the sensitivity of eigenvalues under perturbations, and have several applications.… (More)

- R Hryniv, P Lancaster
- 2007

In this paper behaviour of the spectrum of matrix-valued functions depending analytically on two parameters is studied. Generalizations of the Rellich theorem on analytic dependence of the spectrum and complete regular splitting of multiple eigenvalues are established.