ABSTRACT
Our goal is to convert some of the algorithms of mathematical analysis into computer programs. This requires as much thought and subtlety as devising the algorithms themselves. It is also fraught with hazards, since there is no acceptable procedure for proving that a computer implementation of a nontrivial algorithm is correct. Even if the underlying algorithm is supported by mathematical proof, the peculiarities of computation in practice might still lead to unexpected results. Thus the first part of this chapter is devoted to listing some of the most common problems encountered while transferring mathematical analysis into software.
