The -pseudospectrum of a square matrix A is the set of eigenvalues attainable when A is perturbed by matrices of spectral norm not greater than . The pseudospectral abscissa is the largest real part of such an eigenvalue, and the pseudospectral radius is the largest absolute value of such an eigenvalue. We find conditions for the pseudospectrum to be Lipschitz continuous in the setvalued sense ...

The problem of determining minimum-fuel maneuver sequences for a four-spacecraft formation is considered. The objective of this paper is to determine fuel-optimal configuration trajectories that transfer a four spacecraft formation from an initial parking orbit to a desired terminal reference orbit while satisfying particular formation constraints. In this paper, the configuration problem is so...

This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the Schrödinger equation as examples. This approach transforms the dense system of the pseudospectral discretization approximately into a sparse system via an equivalent i...

A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral me...

Poisson equation is frequently encountered in mathematical modeling for scientific and engineering applications. Fast Poisson numerical solvers for 2D and 3D problems are, thus, highly requested. In this paper, we consider solving the Poisson equation ∇2u = f(x, y) in the Cartesian domain Ω = [−1, 1] × [−1, 1], subject to all types of boundary conditions, discretized with the Chebyshev pseudosp...

We describe Fourier pseudospectral time-domain simulations, carried out in order to study light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to accurately predict the electromagnetic scattering in such problems arises from the discontinuity in the dielectric function along the surface of the metallic object. Standard Fourier methods lead to oscillatory b...

By systematically altering the in-plane flight path and velocity of an aircraft and the rate at which the cable is deployed, the tip of a cable being towed behind an aircraft is shown to rendezvous with a ground-based surface location in minimum time, with minimum control effort required. This is achieved through optimal control, formulated as a nonlinear programming problem using the Legendre-...

In our previous work, we have shown that the pseudospectral method is an effective and flexible computation scheme for deriving pulses for optimal control of quantum systems. In practice, however, quantum systems often exhibit variation in the parameters that characterize the system dynamics. This leads us to consider the control of an ensemble (or continuum) of quantum systems indexed by the s...

The estimate derived by Henshaw, Kreiss, and Reyna for the smallest scale present in solutions of the two-dimensional incompressible Navier-Stokes equations is employed to obtain convergent pseudospectral approximations. These solutions are then compared with those obtained by a number of commonly used numerical methods. If the viscosity term is deleted and the energy in high wave numbers remov...