Abstract
This chapter discusses error analysis. In laboratory practice, exact error analysis is usually omitted. The following are the reasons for this: (1) it is difficult or impossible to carry out, (2) many of the mathematical theorems are irrelevant to machine computation, (3) the estimates are too pessimistic, and (4) it is replaced by an automatic or approximate sort of analysis. Error analysis is the tithe that intelligence demands of action but it is rarely paid. The chapter discusses roundoff errors. Roundoff errors in function values can cause serious difficulties in certain automatic integration routines. A number of methods can be employed to reduce roundoff error when the number of summands is very large. The methods are based upon the fact that when a small number is added to a large number a part of the accuracy inhering in the former will be lost. Successive summands in the integration rules are of the same order of magnitude and, hence, should be combined one with the other. In addition to problems of roundoff error, one must be aware of additional computational pitfalls in the numerical evaluation of integrals and related computations. These include overflow, underflow, and loss of significance.
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