## A Web-Based Library for Testing
the Performance of Numerical Software

This web-based library is hosted by the development group responsible for the
POLYMATH Numerical Analysis Software. More information on POLYMATH is
available from www.polymath-software.com.

#### Introduction

This Internet site provides the user
with a series of test problems that can be used to evaluate and
verify the solutions of numerical problems with a variety of numerical
software programs. This site is under development by
Mordechai
Shacham,
Neima
Brauner, and
Michael
B. Cutlip. Please send comments or questions
on this library to Mordechai
Shacham.

#### General Philosophy

Many of the complex engineering problems
in today's world require the numerical solutions of very complex
sets of equations. It is often assumed that the numerical software
packages and their solution algorithms will find the correct solution
for a given problem OR that warning messages will be issued when
the accuracy and/or correctness of the solution is in doubt. Thus
this library was created to provide a series of benchmark problems
and their detailed solutions so as to enable the user to verify
that numerical software packages and their algorithms are working
properly.

Test problems in this Numerical Problem
Library all have the following characteristics:

- The problems are of various sizes and
difficulty levels
- The equation sets are given in text
files and a variety of formats
- The detailed solutions are given in
Excel and include all the details of problem solution
- Care is given to reporting the initial
conditions of the problems and the final solutions with sufficient
accuracy for adequate comparisons of various solution methods

The current Numerical Problem Library
is organized by problem type. Only the Nonlinear Equations Library has been
completed at this time.

There is an existing Library for Regression assembled by the National
Institute of Standards and Technology that deals with Analysis of Variance,
Linear Regression, and Nonlinear Regression.