Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) which the right-hand-side is comprised of terms correspond to individual 'processes' or 'fluxes'. Frequently, these ODEs characterised by multiple time-scale phenomena due order magnitude differences between contributing processes presence switching, i.e., dominance sub-dominance par...

We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy.

A travelling waves analysis for a polyatomic gas with n internal energy storage modes is performed. In both the frozen ow and the equilibrium limit the existence and the qualitative behaviour of travelling waves are investigated. Methods from geometric singular perturbation theory are used to study these limits.

In this paper, we study the sensitivity and second order perturbation expansions of simple nonzero finite generalized singular values of a complex matrix pair, which is analytically dependent on several parameters. Our results generalize the perturbation analysis given by Sun [J. Comput. Math., 6 (1988), pp. 258–266] for simple nonzero singular values.

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are...