ABSTRACT
In this chapter, the authors consider methods for representing numbers on computers and the errors involved. A round-off error arises in terminating the decimal expansion and rounding. In contrast, the truncation error terminates a process. Most practical problems requiring numerical computation involve quantities determined experimentally by approximate measurements, which are often estimated to a certain number of significant decimal digits. Most practical problems requiring numerical computation involve quantities determined experimentally by approximate measurements, which are often estimated to a certain number of significant decimal digits. The starting point for the application of interval analysis was, in retrospect, the desire in numerical mathematics to be able to execute algorithms on digital computers capturing all the round-off errors automatically and therefore to calculate strict error bounds automatically. Interval arithmetic, when practical, allows rigor in scientific computations and can provide tests of correctness of hardware, and function libraries for floating-point computations.
