In the mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 field of numerical analysis

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

In engineering

Engineering

Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

 and science

Science

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, one often has a number of data points, obtained by sampling

Sampling (statistics)

In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....

 or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e.