Introduction

A frequently applied method for the testing of numerical software is to exercise it on a battery of representative problems. Often such problems are generated randomly, insuring that a large number of test cases can be applied. Unfortunately, this is rarely sufficient for serious numerical software testing. Errors or, more likely, numerical difficulties typically occur for highly structured problems or for those near to the boundaries of applicability of the underlying algorithm. These parts of the domain are rarely sampled in random problem generation, and hence testing must also be done on problem sets which illustrate special behaviors. These are quite difficult to produce, and, thus, groups of researchers often exchange sample problem sets. Such data sets serve a variety of additional purposes:

Defining the state-of-the-art.

Characterizing industrial-grade applications.

Catalyzing research by posing challenges.

Providing a baseline of performance for software developers.

Providing data for users who want to gain confidence in software.

Unfortunately, these collections are often lost when the underlying technology is picked up by the commercial sector, leaving software developers and users without an important tool to use to judge the capability of their products. One of the goals of this project is to identify, preserve, and make readily available such test corpora for use by researchers, developers, and users of mathematical and statistical software. In this paper we describe work that is underway in the area of test data for matrix algorithms.