Abstract
This chapter discusses interpolation and approximation. Interpolation is one of the most basic and most often used numerical techniques. Through the years many interpolation methods have been invented with the aim of simplifying the computations when performed by hand or with a desk calculator. However, a general program based on a Newton divided difference formula is usually sufficient for computer applications. A polynomial of degree n is defined by its n + 1 coefficients. Thus, it is natural to expect that an interpolating polynomial of degree n would be completely determined by (n + 1) function values fk. The number of operations needed to evaluate the Lagrange formula at a single point makes it impractical for many applications. Truncation error and rounding errors are reviewed in the chapter. Some methods for deriving special-purpose interpolation formulas are also discussed. The technique for deriving special types of approximations is called the method of undetermined coefficients. It is a useful device provided the system of equations for determining the coefficients can be solved.
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