David K. Kahaner

GAMS: a framework for the management of scientific software

The Guide to Available Mathematical Software (GAMS) provides a framework for both a scientist-end-user and a librarian-maintainer to deal with large quantities of mathematical and statistical software. This framework includes a classification scheme for mathematical and statistical software, a database system to manage information about this software, and both an on-line interactive consulting system and a printed catalog for providing users with access to this information. A description is given of GAMS and its use at the National Bureau of Standards.

TWODQD an adaptive routine for two-dimensional integration

Abstract This is an adaptive subroutine that computes an approximation to the integral of a function f ( x, y ) over a two dimensional region made up of triangles. Lyness–Jespersen rules form the basis for a local quadrature module that is used to estimate the integral and the error over each triangle. The triangle with the largest error is subdivided and the local quadrature module is applied to each sub-triangle to obtain new estimates of the integral and the error. This process is repeated until either (1) an error tolerance is satisfied, (2) the number of triangles exceeds an input parameter MAXTRI, (3) the number of integrand evaluations exceeds an input parameter MEVALS, or (4) the subroutine senses that round-off error is beginning to contaminate the result.

The guide to available mathematical software problem classification system

A vast collection of reusable mathematical and statistical software is now available for use by scientists and engineers in their modeling efforts. This software represents a significant source of mathematical expertise, created and maintained at considerable expense. Unfortunately, the collection is so heterogeneous that it is a tedious and error-prone task simply to determine what software is available to solve a given problem. In mathematical problem solving environments of the future such questions will be fielded by expert software advisory systems. One way for such systems to systematically associate available software with the problems they solve is to use a problem classification system. In this paper we describe a detailed tree-structured problem-oriented classification system appropriate for such use.

Virtual reality in Japan

The trends of virtual-reality research in Japan are reviewed. Research on the application of virtual reality systems in three-dimensional imaging of software structures, remote control of construction robots, and molecular model design is discussed. A prototype of a plant monitoring system that uses camera images to provide a sense of being there, and experiments on the tactile senses of touch and pressure, are described. The space interface device for artificial reality (SPIDAR) is also discussed.<<ETX>>

The numerical evaluation of certain multivariate normal integrals

Abstract We show that a multivariate normal integral with tridiagonal covariance matrix can be computed efficiently using iterated integration.

On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems

We discuss how rootfinding, which is built into some ODE software, can be used to generate Poincare sections. An interactive program is also described.

Mathematical software: Plod

The authors present Plod (plotted solutions of ordinary differential equation), mathematical software Fortran package designed by integrating large systems of equations that are unstable with respect to initial conditions (stiff). It is intended for microcomputer users unfamiliar with programming techniques. The hardware needed to run Plod is described. Plod is designed to be used in two interactive steps, and an example of each is given. Graphics capabilities and extensibility are briefly considered.<<ETX>>

Mathematical Software in Basic Evaluation of Definite Integrals

This program for the numerical approximation of definite integrals has been tested in several microcomputer environments. It is competitive with similar mathematical software in Fortran.

Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared-memory parallel computer

Abstract We consider method of lines solutions of partial differential equations on shared-memory parallel computers. Solutions using the ordinary differential equation solver SDRIV3 (which is similar to the well-known LSODE solver) are considered. It is shown that portions of the solver may be implemented in parallel. In particular, formation of the Jacobian matrix and the linear algebra required to solve the corrector equations are natural candidates for parallel implementation since these portions dominate the cost of solving large systems of equations. A variant of Gaussian elimination is described which allows efficient parallel solution of systems of linear equations. An implementation of SDRIV3 which performs the Jacobian related calculations in parallel and which uses this variant of Gaussian elimination is described. The modified solver is used to solve a model hyperbolic fluid flow problem. Timing results, obtained using a Sequent Balance parallel computer, are given which demonstrate that substantial speedups are possible. Extensions of the techniques to sparse problems are discussed and illustrated for a problem involving a humidification column which contacts air and water.

The GAMS classification scheme for mathematical and statistical software

An extensive tree-structured problem-oriented scheme for classifying mathematical and statistical software is presented. The scheme is a substantially modified version of a scheme proposed by Bolstad, which was based on the widely-used SHARE system. It is an attempt to reflect more accurately the current state of mathematical and statistical software. Our changes resulted from using the Bolstad scheme as the basis for the NBS Guide to Available Mathematical Software (GAMS), which provides NBS scientists information about subprograms in the IMSL, NAG, and PORT libraries, and in dozens of public-domain subprogram packages.