We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use them to stabilize numerical calculations. Our method follows classical analysis for first-order systems and higherorder scalar equations where growth behavior is expressed in terms of elementary functions. We then recast our equations in mollified form thereby obtaining stabi...

Applications such as the modal analysis of structures and acoustic cavities require a number of eigenvalues and eigenvectors of large scale Hermitian eigenvalue problems. The most popular method is probably the spectral transformation Lanczos method. An important disadvantage of this method is that a change of pole requires a complete restart. In this paper, we investigate the use of the ration...

Several algorithms have been proposed in the literature for the computation of the zeros of a linear system described by a state-space model 1x1 A,B,C,D}. In this report we discuss the numerical properties of a new algorithm and compare it with some earlier techniques of computing zeros. The new approach is shown to handle both nonsquare and/or degenerate systems without difficulties whereas ea...

We have developed a 3-D Eulerian hydrodynamics code to model sources of gravitational radiation. The code is written in cylindrical coordinates (̟, z, φ) and has moving grids in the ̟ and z-directions. We use Newtonian gravity and calculate the gravitational radiation in the quadrupole approximation. This code has been tested on a variety of problems to verify its accuracy and stability, and the ...

Software for computing eigenvalues and invariant subspaces of general matrix products is proposed. The implemented algorithms are based on orthogonal transformations of the original data and thus attain numerical backward stability, which enables good accuracy even for small eigenvalues. The prospective toolbox combines the efficiency and robustness of library-style Fortran subroutines based on...

A new theoretical Evans function condition is used as the basis of a numerical test of viscous shock wave stability. Accuracy of the method is demonstrated through comparison against exact solutions, a convergence study, and evaluation of approximate error equations. Robustness is demonstrated by applying the method to waves for which no current analytic results apply (highly nonlinear waves fr...

We consider two models commonly used in the literature to model adversarial injection of packets into a packet switching network. We establish the relation between these two types of models, and between them and the set of sequences of packets that allow stability. We also consider the adaptive setting in which packets are injected with only their source and destination but without a prescribed...

This paper describes a partial differential equation for denoising images. The proposed method is demonstrably superior to anisotropic diffusion (and it’s many variations) for denoising images that are approximately piecewise constant. The method relies on an equation that is the level-set equivalent of the anisotropic diffusion equation proposed by Perona and Malik [1]. This proposed equation ...

This short note points out an improvement on the robust stability analysis for electrically driven robots given in the paper. In the paper, the author presents a FAT-based direct adaptive control scheme for electrically driven robots in presence of nonlinearities associated with actuator input constraints. However, he offers not suitable stability analysis for the closed-loop system. In other w...

This short note points out an improvement on the robust stability analysis for electrically driven robots given in the paper. In the paper, the author presents a FAT-based direct adaptive control scheme for electrically driven robots in presence of nonlinearities associated with actuator input constraints. However, he offers not suitable stability analysis for the closed-loop system. In other w...