ABSTRACT
This chapter is concerned with the basic ideas from numerical analysis that enter into statistical computation. Numerical analysis is concerned with the properties of numerical algorithms, particularly their convergence, their stability, and the size of possible errors in the result. The particular set of representable numbers depends upon the floating-point format implemented on a computer system. A floating-point format together with rules for performing arithmetic operations on numbers in that format constitutes a floating-point system. Most large computers have at least one floating-point system implemented in the machine's hardware. Most of the microprocessors on which personal computers and scientific workstations are based have only limited fixed-point arithmetic operations as part of the basic instruction set. As a consequence, floating-point computations must be carried out either in software, or in special-purpose numerical data processors. The floating-point standard differs in several important respects from the hardware floating-point systems contained in most mainframe computers.
