Fundamentals of Computational Methods for Engineers

Interpolation, Curve Fitting, and Approximation

Author(s): Tanvir Ahmed* and Masud Rana

Pp: 65-102 (38)

DOI: 10.2174/9789815039054122010006

* (Excluding Mailing and Handling)


In this chapter, we study numerical techniques that deal with given set of data points arising from experimental works. Starting from linear interpolation, different interpolating polynomials are discussed that are used to find functional value at intermediate points of the given data set. Lagrange interpolation is discussed that does not require equally spaced data points. Newton forward and backward difference interpolation formulae are derived to evaluate function near the beginning and end parts of the given data sets. Linear least-squares fit that is widely used to approximate unknown functions is presented and an algorithm is developed. We also discuss least-squares approximations for approximating an explicit function on given interval.

Keywords: Interpolation, Extrapolation, Polynomial curve fitting, Approximation.

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