We propose a fast and stable numerical method to evaluate two-dimensional partial differential equation (PDE) for pricing arithmetic average Asian options. The numerical method is deduced by combining an alternating-direction technique and the central difference scheme on a piecewise uniform mesh. The numerical scheme is stable in the maximum norm, which is true for arbitrary volatility and arb...

Luca Gammaitoni,1 Markus Löcher,4 Adi Bulsara,2 Peter Hänggi,3 Joseph Neff,4 Kurt Wiesenfeld,4 William Ditto,4 and Mario E. Inchiosa2 1Dipartimento di Fisica, Universitá di Perugia and Instituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06100 Perugia, Italy 2Space and Naval Warfare Systems Center San Diego, Code D-364, San Diego, California 92152-5001 3Institut für Physik, Universität...

By J. Douglas, Jr., R. B. Kellogg, and R. S. Varga We consider the iterative solution of the system of linear equations (1 ) (Xi + X-, + • ■ ■ + Xn)z = /, n 2; 2, where each Xj, 1 | j | n, is a Hermitian and positive definite N X N matrix. If n = 2, the iterative methods of Peaceman-Rachford [1, Chapter 7], or D'yakonov [2] and Kellogg [3], may be used to solve (1). In this paper these methods ...

We investigate the factored ADI iteration for large and sparse Sylvester equations. A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration. The application to generalized Sylvester equations is considered as well. We also discuss the efficie...

This paper shows how a well-balanced trade-off between a generic workstation and dumb but fast reconfigurable hardware can lead to a more efficient implementation of a cryptanalysis than a full hardware or a full software implementation. A realistic cryptanalysis of the A5/1 GSM stream cipher is presented as an illustration of such trade-off. We mention that our cryptanalysis requires only a mi...

The modified Szabo wave equation is one of the various models that have been developed to model the power law frequency-dependent attenuation phenomena in lossy media. The purpose of this study is to develop two different efficient numerical methods for the two-dimensional Szabo equation and to compare the relative merits of each method. In both methods we employ the ADI scheme to split directi...

This study investigates the frequency-dependence of fluid flow in heterogeneous porous media using the theory of dynamic penneability and a finite-difference method. Given a penneability distribution, the dynamic penneability is applied locally to calculate the frequency-dependence of fluid flow at each local point. An iterative Alternating Direction Implicit finite-difference technique is appl...

1. Introduction. This note presents a few of the results which we have obtained by applying a classical and fundamental idea to the analysis of certain partial difference equations. The idea is that certain multidimensional problems can be solved by solving a few one-dimensional problems—it is the basis of the classical method of separation of variables of mathematical physics. In the case of p...

This issue of Wireless Security Perspectives focuses on GSM and the December 1999 article titled Real Time Cryptanalysis of the Alleged A5/1 on a PC (preliminary draft) by Alex Biryukov and Adi Shamir. The authors describe an attack on the GSM A5/1 traffic encryption algorithm and claim that by analyzing the output of the algorithm, one can recover the cryptographic key in less than a second us...