There are two laws of scientific computing:

- A good numerical method gives you the exact solution to a nearby problem. (Nick Trefethen prefers ``A good numerical method gives you nearly the right solution to nearly the right problem'', and indeed the distinction is important; however, a great many actual algorithms really do give you exact solutions of nearby problems.)
- Some problems are sensitive to changes.

These principles are useful because if a computer program gives you a bad answer to a problem, it isn't immediately clear that it is the computer program's `fault'. Sometimes, the problem itself is to blame. The question is, when?

The first principle gives us a practical way to decide, in any given problem context. The second principle reminds us that some problems are bad. This will become clearer with examples.

Before we begin the examples, I mention the premier software
package for solving linear systems of equations.

Wed Jan 31 11:33:59 EST 1996