Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time der...

We discuss the estimation of the asymptotic covariance matrix of semiparametric maximum likelihood estimators by the observed proole information. We show that a discretized version of the second derivative of the proole likelihood function yields consistent estimators of minus the eecient information matrix.

In Tikhonov-Phillips regularization of general form the given ill-posed linear system is replaced by a Least Squares problem including a minimization of the solution vector x, relative to a seminorm ‖Lx‖2 with some regularization matrix L. Based on the finite difference matrix Lk, given by a discretization of the first or second derivative, we introduce the seminorm ‖LkD x̃ x‖2 where the diagona...

A class of new observers in descriptor linear systems, proportional-derivative (PD) observers, are proposed. A parametric design approach for such observers is proposed based on a complete parametric solution to the generalized Sylvester matrix equation. The approach provides complete parameterizations for all the observer gains, gives the parametric expression for the corresponding left eigenv...

We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standin...

Existing algorithms for computing the matrix cosine are tightly coupled to a specific precision of floating-point arithmetic optimal efficiency so they do not conveniently extend an arbitrary environment. We develop algorithm that takes unit roundoff working as input, and works in precision. The employs Taylor approximation with scaling recovering it can be used Schur decomposition or decomposi...