The departure from normality of a matrix plays an essential role in numerical matrix computations since it rules the spectral instability. But this rst consequence of high nonnormality was for long considered by practioners as a mathematical oddity, since such matrices were not often encountered in practice. It appears now that more and more matrices, which have a possibly unbounded departure f...

This paper proposes a new approach for computing the Lyapunov Characteristic Exponents (LCEs) for continuous dynamical systems in an ecient and numerically stable fashion. The method is adapted to systems with small dimensions. Numerical examples illustrating the accuracy of method are presented.

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

Compressive principal component pursuit (CPCP) recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. Pervious works mainly focus on the analysis of the existence and uniqueness. In this paper, we address its stability. We prove that the solution to the related convex programming of CPCP gives an estimate that is stable to small en...

A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is developed for systems of partial differential equations with polynomial nonlinearities. The framework is rather general and allows for an arbitrary number of depe...

In order for a patient to be discharged from a hospital unit, a physician must first perform a physical examination and review the pertinent medical information to determine that the patient is stable enough to be transferred to a lower level of care or be discharged home. Requiring an inspection of a patient’s ‘readiness for discharge’ introduces an interesting dynamic where patients may occup...

For distinct primes / and p , the Iwasawa invariant XT stabilizes in the cyclotomic Zp -tower over a complex abelian base field. We calculate this stable invariant for p = 3 and various / and K. Our motivation was to search for a formula of Riemann-Hurwitz type for XT that might hold in a p-extension. From our numerical results, it is clear that no formula of such a simple kind can hold. In the...

Unwanted relative vibrations between the tool and the workpiece represent significant challenges in high-speed machining. In order to avoid this problem, one needs to specify ranges for system parameters (spindle speed, depth of cut) for which the process is stable, i.e., to obtain a so-called stability chart. Such stability charts usually can only be given by numerical means which is illustrat...

We carry out a systematic numerical stability analysis of ZND detonations of Majda’s model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat release and activation energy are varied. Our purpose is, first, to answer a question of Majda whether oscillatory instabilities can occur for high activation energies as in the full reacting Euler equations, and, second,...

Vector fitting is widely accepted as a robust macromodelling tool for efficient frequency domain identification of passive components. The orthonormal vector fitting technique is introduced, which improves the numerical stability of the method, by using orthonormal rational functions. This leads to better conditioned equations, reduces the numerical sensitivity to the choice of starting poles s...