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.
Linear interpolation is a method used to estimate unknown values that fall within two known values in a dataset, assuming that the change between values is linear. It is widely used in numerical analysis and computer graphics to construct new data points within the range of a discrete set of known data points.
Newton's Divided Differences is a method for constructing polynomial interpolants of a given set of data points, allowing for efficient computation of coefficients in Newton's interpolating polynomial form. This approach is particularly useful for its recursive nature and its ability to handle unequally spaced data points, making it a versatile tool in numerical analysis.
Piecewise functions are defined by multiple sub-functions, each applying to a specific interval of the domain, allowing for the modeling of complex behaviors that change over different ranges. They are essential in scenarios where a single expression cannot adequately describe a situation, such as in cases of step functions or absolute value functions.
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.