Interpolation, Curve Fitting, and Approximation

- Authors: Tanvir Ahmed1, Masud Rana2
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View Affiliations Hide AffiliationsAffiliations: 1 Department of Electrical & Electronic Engineering, Rajshahi University of Engineering & Technology, Bangladesh 2 Department of Electrical & Electronic Engineering, Rajshahi University of Engineering & Technology, Bangladesh
- Source: Fundamentals of Computational Methods for Engineers , pp 65-102
- Publication Date: May 2022
- Language: English
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.
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