We develop a new algorithm for the computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of the problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable conditioning and backward stability properties, and a preprocessing step that reveals and deflates the zero and infinite eigenvalues contributed by singular leading and trailing matrix coefficients. The algorithm is backward stable for quadratics that are not too heavily damped. Numerical experiments show that our MATLAB implementation of the algorithm, quadeig, outperforms the MATLAB function polyeig in terms of both stability and efficiency.

Given a pair of distinct eigenvalues (λ 1 , λ 2) of an n×n quadratic matrix polynomial Q(λ) with nonsingular leading coefficient and their corresponding eigenvectors, we show how to transform Q(λ) into a quadratic of the form Q d (λ) 0 0 q(λ)

Allergic disease is a growing health risk in the modern world, while its management at professional and patients' levels is unsatisfactory. There is no register of prevalence and biopsychosocial co-factors of allergic reactions as they occur in real world settings. The Allergic Reactions in the Community (AlleRiC) study aims to develop and validate an on-line questionnaire to allow real time food allergic reactions to be reported, with scope for an in depth exploration of related real-world factors.

No abstract