Abstract
This chapter focuses on numerical approximation. The derivation of numerical results usually involves approximation. Some of the most common reasons for approximation are round-off error, the use of interpolation, the approximate values of elementary functions generated by computer sub-routines, the numerical approximation of definite integrals, and the numerical solution of both ordinary and partial differential equations. The chapter outlines some of the most frequently used methods of approximation, ranging from linear interpolation, spline function fitting, the economization of series and the Fade approximation of functions, to finite difference approximations for ordinary and partial derivatives. When interpolation is necessary and more than three data points are involved, a possible approach is to use the Lagrange interpolation polynomials between successive groups of three data points. Cubic spline interpolation is the most frequently used form of spline interpolation, and it is particularly useful when a smooth curve needs to be generated between known fixed points.
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