A computationally intensive part in a model for numerical weather forecasting solves a set of partial di erential equations. There are several techniques to obtain this solution numerically. In this paper we will discuss the implementation of a numerical weather forecasting model on a massively parallel architecture using two techniques: a nite di erence (gridpoint) method and a spectral method...

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...

The nite di erence method is a numerical analysis technique used to solve problems involving irregular geometries, complicated boundary conditions, or both. The geometries are represented using partial di erential equations. The solutions to the partial di erential equations can be easily generated with the aid of a computer. As the geometries become increasingly complex, the solutions of the p...

We discuss the temporal-di erence learning algorithm, as applied to approximating the cost-to-go function of an in nite-horizon discounted Markov chain. The algorithm we analyze updates parameters of a linear function approximator on{line, during a single endless trajectory of an irreducible aperiodic Markov chain with a nite or in nite state space. We present a proof of convergence (with proba...

6.1 A Basic Statistical Method in Hypothesis Testing. In chapter 4 we encountered our …rst problems in statistical inference. One dealt with the problem of sample size. The other was a problem of a statistical test of hypothesis. It dealt with the problem of whether two samples arose from the same distribution function or whether there was a shift and essentially a di¤erence in means between th...

The ultimate goal of this research is to construct a hybrid model for sound propagation in layered underwater environments with curved boundaries by employing a di↵erential formulation for inhomogeneous layers and a boundary integral formulation for homogeneous layers. The discretization of the new hybrid model is a combination of a finite di↵erence method for the Helmholtz equation for inhomog...

The computation of large sparse Jacobian matrices is required in many important large-scale scienti c problems. We consider three approaches to computing such matrices: hand-coding, di erence approximations, and automatic di erentiation using the ADIFOR (Automatic Di erentiation in Fortran) tool. We compare the numerical reliability and computational e ciency of these approaches on applications...

This article documents my journey down the rabbit hole, chasing what I have come to know as a particularly unyielding problem in Ramsey theory on the integers: the 2-Large Conjecture. This conjecture states that if D ✓ Z+ has the property that every 2-coloring of Z+ admits arbitrarily long monochromatic arithmetic progressions with common di↵erence from D then the same property holds for any fi...

A new approach was developed for the analysis of problems of physics governed by laws of conservation. The methodology establishes an analogy between various aspects of evolution and genetics of life processes and inanimate physical systems. This analogy is then used to generate solutions to physical problems in a similar way to which organisms in nature solve problems imposed by environmental ...

A beamforming array is investigated for use in a radar system that is part of a hybrid acoustic/electromagnetic technique for detecting land mines. The radar is used to measure the surface displacement of the earth due to acoustic waves in the earth. The beamforming array is used to obtain small spatial resolution for the measurement of the displacement while allowing an adequate stando distanc...