Interpolation

Interpolation estimates values within the range of known data points by fitting or selecting a rule that connects them.

Linear interpolation: A method that estimates values between two data points by connecting them with a straight line. It is the simplest rule: each interval is treated as a straight segment.
Data point: A recorded value paired with its position in a dataset or domain. Interpolation starts from known values at specified input positions.
Image scaling: Changing an image’s pixel dimensions by resampling its discrete pixel grid. Resampling estimates pixel colors at locations that were absent from the original grid.
Regression analysis: A statistical approach that models relationships between variables, typically minimizing a measure of residual error. Regression usually tolerates nonzero residuals, whereas interpolation matches supplied points exactly.
Polynomial interpolation: A method that fits a polynomial through a finite set of data points. A single polynomial can pass exactly through every supplied point.
Independent variable: A variable whose value is selected or observed as an input to a relationship. Its known positions determine where interpolation is anchored and where estimates are requested.
Resampling (statistics): A family of methods for generating new samples from observed data or a fitted distribution. Interpolation can create intermediate observations when a sampled signal is shifted or resized.
Smoothing: A set of methods that reduces short-scale variation in data to reveal broader patterns. Smoothing may deliberately miss observed values rather than pass through every point.
Lagrange polynomial: A polynomial expressed as a weighted sum of basis polynomials, each equal to one at a selected data point and zero at the others. Its basis formula constructs the unique interpolating polynomial directly from the points.
Function: A rule assigning each permitted input exactly one output. An interpolation rule supplies a function-like estimate across gaps in the data.

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