An initial value problem with piecewise constant coe cients is considered. The accuracies for both nite di erence methods and the pseudospectral method are analyzed, and a modi cation of the initial value problem is suggested. The modi ed problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method at integ...

We present a pseudospectral formulation of the multireference single and double excitation configuration interaction method. A formal scaling advantage is achieved and practical timings are presented. The accuracy of the pseudospectral approximation within this method is probed for a variety of test cases. The method is typically accurate to within 1 mhartree while being up to six times faster ...

The pseudospectral abscissa and the stability radius are well-established tools for quantifying the stability of a matrix under unstructured perturbations. Based on first-order eigenvalue expansions, Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192] recently proposed a linearly converging iterative method for computing the pseudospectral abscissa. In this paper, we pr...

In this paper, an optimal trajectory guidance law is developed for a free-floating space manipulator through a combination of a Gaussian pseudospectral collocation scheme with a Non-Linear Problem solver. Specifically, the resulting nonlinear optimal guidance problem with path constraints is defined with the general pseudospectral optimal software and numerically solved by the sparse nonlinear ...

When pseudospectral approximations are used for space derivatives, one often encounters spurious eigenvalues. These can lead to severe time stepping difficulties for PDEs. This is especially the case for equations with high order derivatives in space, requiring multiple conditions at one or both boundaries. We note here that a very simple-to-implement fictitious point approach circumvents most ...

A method is presented for direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using global collocation at Legendre-Gauss-Radau (LGR) points. A key feature of the method is that it provides an accurate way to map the KKT multipliers of the nonlinear programming problem to the costates of the optimal control problem. More precisely...

The -pseudospectrum of a matrix A is the subset of the complex plane consisting of all eigenvalues of all complex matrices within a distance of A. We are interested in two aspects of “optimization and pseudospectra.” The first concerns maximizing the function “real part” over an -pseudospectrum of a fixed matrix: this defines a function known as the -pseudospectral abscissa of a matrix. We pres...