This paper introduces a new numerical method for integration of ordinary differential equations. Following the idea of quantization based integration, i.e., replacing the time discretization by state quantization, this new method performs a third order approximation allowing to achieve better accuracy than their first and second order predecessors. It is shown that the new algorithm satisfies t...

This project demonstrates two basically different methods for Image Band Compression as applications of Linear Algebra and compares them. The first method describes the application of Singular Value Decomposition (SVD) in Image Band Compression using minimum best rank approximation technique. The second method uses Vector Quantization (VQ) method to compress image using Self-Organizing Maps (SO...

We propose a new Quantization algorithm for the approximation of inhomogeneous random walks, which are the key terms for the valuation of CDO-tranches in latent factor models. This approach is based on a dual quantization operator which posses an intrinsic stationarity and therefore automatically leads to a second order error bound for the weak approximation. We illustrate the numerical perform...

In this paper we consider electromagnetic field quantization in the presence of a dispersive and absorbing semiconductor quantum dot. By using macroscopic approach and Green's function method, quantization of electromagnetic field is investigated. Interaction of a two-level atom , which is doped in a semiconductor quantum dot, with the quantized field is considered and its spontaneous emission ...

We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large in such small systems. Although a Fokker-Planck equation obtained by the system size expansion includes the fluctuation effects, it needs large computational ...