Interpolation, Regression, and Smoothing
Interpolation and regression of data and smoothing of noisy data play a significant role in many scientific disciplines. Interpolation is an estimation of an unknown variable at output points (locations) by employing the known values at surrounding input points. Regression is an estimation of a variable at both input and output points by employing the known values at the surrounding input locations. Smoothing is an estimation of a variable at only known input points by employing the known input values. Smoothing may be necessary if the input data is noisy. It is worth noting that interpolation is different than regression and smoothing; the estimation based on interpolation passes through all the known input values. In other words, there is an exact recovery of the known values of the input points. There exist several methods for such estimations.