There are two laws of scientific computing:
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.