that I have read this dissertation and that in my opinion it is fully adequate,

The derivation of low-storage, explicit Runge–Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier–Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, sixteen ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been tested with not only DETEST, but also with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be nearly matched while still saving 2–3 registers of memory.

Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known Painlev e test, which is applicable to polynomial systems of ordinary and partial differential equations. The second and third algorithms allow one to explicitly compute polynomial conserved densities and higher-order symmetries of nonlinear evolution and lattice equations. The first algorithm is implemented in the symbolic syntax of both Macsyma and Mathematica. The second and third algorithms are available in Mathematica. The codes can be used for computer-aided integrability testing of nonlinear di erential and lattice equations as they occur in various branches of the sciences and engineering. Applied to systems with parameters, the codes can determine the conditions on the parameters so that the systems pass the Painlevé test, or admit a sequence of conserved densities or higher-order symmetries...

An algorithm to compute polynomial conserved densities of polynomial nonlinear lattices is presented. The algorithm is implemented in Mathematica and can be used as an automated integrability test. With the code didens.m, conserved densities are obtained for several well-known lattice equations. For systems with parameters, the code allows one to determine the conditions on these parameters so that a sequence of conservation laws exist. Keywords: Conservation law; Integrability; Semi-discrete; Lattice 1 Introduction There are several motives to nd the explicit form of conserved densities of dierential-dierence equations (DDEs). The rst few conservation laws have a physical meaning, such as conservation of momentum and energy. Additional ones facilitate the study of both quantitative and qualitative properties of solutions [1]. Furthermore, the existence of a sequence of conserved densities predicts integrability. Yet, the nonexistence of polynomial conserved quantities does not p...

We study the high-performance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three “sweeps”: a Cholesky factorization of the SPD matrix, the inversion of the resulting triangular matrix, and finally the multiplication of the inverted triangular matrix by its own transpose. We state different algorithms for each of these sweeps as well as algorithms that compute the result in a single sweep. One algorithm outperforms the current ScaLAPACK implementation by 20-30 percent due to improved load-balance on a distributed memory architecture.

When considering the unmanageable complexity of computer systems, Dijkstra recently made the following observations: 1. When exhaustive testing is impossible -- i.e., almost always -- our trust can only be based on proof (be it mechanized or not). 2. A program

Introduction Model selection is a central task in computer vision: given data obtained from images and given a number of models, which model is most strongly supported by the data? Is it better to have i) a simple model fitting the data approximately; or ii) a complicated model fitting the data very closely [3],[4], [9],[11]? In many cases the models vary widely in complexity and flexibility, and there is little prior knowledge about the best choice of model. The Minimum Description Length (MDL) method links model selection to data compression: the best model is the one which yields the largest compression of the data. The general theoretical framework for compression is Kolmogorov complexity: let x, y be bit strings, ie. elements of \Sigma = f0; 1g . The Kolmogorov complexity K(xjy) of x conditional o

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Grid computing has great potential but to enter the mainstream it must be simplified. Tools and libraries must make it easier to solve problems by being simpler and at the same time more sophisticated. In this paper we describe how Grid computing can be achieved through spreadsheets. No parallel programming or complex tools need to be used. So long as dependencies allow it, formulae in a spreadsheet can be evaluated concurrently on the Grid. Thus Grid computing becomes accessible to all those who can use a spreadsheet. The story is completed with a sophisticated backend system, NetSolve, which can solve complex linear algebra systems with minimal intervention from the user. In this paper we present the architecture of the system for performing such simple yet sophisticated grid computing and a case study which performs a large singular value decomposition. 1.

This paper considers the problem of certifying the reliability of a software system that can be decomposed into a finite number of modules. It uses a Markovian model for the transfer of control between modules in order to develop the system reliability expression in terms of the module reliabilities. A test procedure is considered in which only the individual modules are tested and the system is certified if, and only if, no failures are observed. The minimum number of tests required of each module is determined such that the probability of certifying a system whose reliability falls below a specified value R 0 is less than a specified small fraction b. This sample size determination problem is formulated as a two-stage mathematical program and an algorithm is developed for solving this problem. Two examples from the literature are considered to demonstrate the procedure. Keywords: Software reliability; Modular Tests; Sample Size Determination; Mathematical Programming 1 1. Introduc...