Non-linear interpolation is a method used to estimate values between two known data points by fitting a curve, rather than a straight line, through the data points. This approach is particularly useful when the data exhibits a non-linear trend, allowing for more accurate predictions in complex datasets.
Barycentric interpolation is a method for polynomial interpolation that is computationally efficient and numerically stable, especially advantageous for high-degree polynomials. It leverages the barycentric weights to simplify the interpolation process, avoiding the need for recalculating polynomial coefficients when adding or removing data points.
Piecewise interpolation involves constructing a function that passes through a given set of points by defining different polynomial functions for each interval between points. This method is particularly useful for creating smooth curves that accurately represent data points, especially when the data exhibits varying trends or rates of change across different intervals.