During recent years a great deal of interest has been devoted to large scale computing applications. This has occurred in great part because of the introduction of advanced high performance computer architectures. The book contains survey articles as well as chapters on specific research applications, development and analysis of numerical algorithms, and performance evaluation of algorithms on advanced architectures. The effect of specialized architectural features on the performance of large scale computation is also considered by several authors. Several areas of applications are represented, including the numerical solution of partial differential equations, iterative techniques for large structured problems, the numerical solution of boundary value problems for ordinary differential equations, numerical optimization, and numerical quadrature. Mathematical issues in computer architecture are also presented, including the description of grey codes for generalized hypercubes. The results presented in this volume give, in our opinion, a representative picture of today’s state of the art in several aspects of large scale computing.

chapter |33 pages

On the Gauss-Broyden Method for Nonlinear Least Squares

ByAndreas Griewank, Laihua Sheng

chapter |13 pages

Parallel Adaptive Algorithms for Multiple Integrals

ByAlan Genz

chapter |31 pages

A Comparison of Hypercube Implementations of Parallel Shooting

ByHerbert B. Keller, Paul Nelson

chapter |34 pages

An Asymptotic Induced Numerical Method for the Convection-Diffusion-Reaction Equation

ByJeffrey S. Scroggs, Danny C. Sorensen

chapter |12 pages

The Rate of Convergence of the Modified Method of Characteristics for Linear Advection Equations in One Dimension

ByClint N. Dawson, Todd F. Dupont, Mary F. Wheeler

chapter |22 pages

Implementation of Finite Element Alternating-Direction Methods for Vector Computers

ByS. V. Krishnamachari, L. J. Hayes

chapter |14 pages

Generalized Gray Codes and Their Properties

ByLinda S. Barasch, S. Lakshmivarahan, Sudarshan K. Dhall

chapter |47 pages

Nested Block Factorization Preconditioners for Convective-Diffusion Problems in Three Dimensions

ByG. K. Leaf, M. Minkoff, J. C. Díaz

chapter |45 pages

A Survey of Spline Collocation Methods for the Numerical Solution of Differential Equations

ByGraeme Fairweather, Daniel Meade