What Is a Template?

A template will include some or all of the following information:

• A high-level description of an algorithm.
• A description of when the algorithm is effective, including conditions on the input and estimates of the time, space, or other resources required. If there are natural competitors, they will be referenced.
• A description of available refinements and user-tunable parameters, as well as advice on when to use them.
• A way to assess the accuracy.
• Numerical examples, illustrating both easy and difficult cases.
• Pointers to complete or partial implementations, perhaps in several languages or for several computer architectures.
• Pointers to texts or journal articles for further information.

This level of description is used for iterative methods where the details are needed to use the algorithm effectively. We have deliberately used the word ``template'' instead of ``numerical recipe'' to emphasize that the methods cannot be used blindly, and that instead knowledge of both the problem and algorithm is needed to effectively solve the problem. ``Black box'' methods that are most suitable for small- to medium-sized problems are described in less detail.