Interpolation constructs a function agreeing exactly with prescribed values at sample points. The resulting function is an interpolant. Choosing a family determines how missing values are filled: polynomial interpolation selects a polynomial, while linear interpolation joins adjacent samples by straight segments. The McShane extension theorem instead permits any Lipschitz function with a specified bound and provides envelopes controlling all allowed choices.
Interpolation is a mathematical and statistical technique used to estimate unknown values that fall within a range of known values. In other words, it involves constructing new data points within the bounds of a discrete set of known data points. There are several methods of interpolation, including: 1. **Linear Interpolation**: It assumes that the change between two points is linear and estimates the value of a point on that line. 2. **Polynomial Interpolation**: This method uses polynomial functions to construct the interpolation function.
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