THE VALIDATION OF NUMERICAL COMPUTATIONS

This chapter discusses the validation of numerical computations. It can never be known with absolute certainty that whether the answers from a numerical computation are correct or not; there is always the possibility that the underlying physical theories are wrong, that the real-world data used are wrong, or that the computer hardware malfunctions. However, the uncertainty substantially can be reduced by using a variety of techniques discussed in the chapter. It is normally expensive to validate the results of a numerical computation. Just to make one reasonable error estimate normally doubles the computational cost. The analysis and checking of a computation for the presence of all types of errors and uncertainties can easily increase the cost by an order of magnitude. There are applications where extreme measures are required, such as nuclear power plant design, air traffic control, manned space flight systems, etc.; in each instance the programmer or user of numerical software should make a conscious decision about the amount of effort to be put into validating the software and its results. Experience shows that time and time again this aspect of computation is slighted. A programmer is so excited when a program finally runs correctly a couple of times that he or she pronounces it finished, completely checked out, and certified. In fact, the program might be such that it gives correct results only about half the time.