abstract The singular value decomposition has a number of applications in digital signal processing. However, the the decomposition must be computed from a matrix consisting of both signal and noise. It is therefore important to be able to assess the eeects of the noise on the singular values and singular vectors | a problem in classical perturbation theory. In this paper we survey the perturba...

The control problem of a robot manipulator with flexures both in the links and joints was investigated using the singular perturbation technique. Owing to the combined effects of the link and joint flexibilities, the dynamics of this type of manipulator become more complex and under-actuated leading to a challenging control task. The singular perturbation being a successful technique for solvin...

In this paper we show that stability for holomorphic vector bundles are equivalent to the existence of solutions to certain system of Monge Amp ere equations parametrized by a parameter k. We solve this fully nonlinear elliptic system by singular perturbation technique and show that the vanishing of obstructions for the perturbation is given precisely by the stability condition. This can be int...

The renormalization group (RG) method for differential equations is one of the perturbation technique proposed by Chen, Goldenfeld, and Oono [1,2]. The RG method unifies traditional singular perturbation methods, such as the multi-scaling method, the boundary layer theory , the averaging method, the normal form theory, the center manifold theory, and the geometric singular perturbation. Chiba [...

We propose a simple and quite efficient code to solve singular perturbation problems when the perturbation parameter ǫ is very small. The code is based on generalized upwind methods of order ranging from 4 to 10 and uses highly variable stepsize to fit the boundary regions with relatively few points. An extensive numerical test section shows the effectiveness of the proposed technique on linear...

in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. thomas algorithm is used to solve the tri-diagonal system. the stability of the algorithm is investigated. it ...

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...