Interpolation

Interpolation

Interpolation is a mathematical technique used to estimate an intermediate value of a quantity that falls between marked values in a series. This method is commonly used in various fields, including science, engineering, and statistics.

In simple terms, interpolation involves determining the value of an unknown data point that lies within a known set of data points. For instance, if a ruler is marked in eighths of an inch, and the measured length falls between 3/8 inch and 1/2 inch, the estimated (interpolated) value might be said to be 7/16 inch.

Interpolation can be linear or non-linear, and there are various methods used to compute the value of the unknown data point. These methods range from simple linear interpolation to more complex techniques such as Lagrange’s formula, spline interpolation, and polynomial interpolation.

Interpolation is a fundamental technique used to fill in missing or incomplete data points, smooth out fluctuations in data, and predict future values. It is a vital tool in scientific research, data analysis, and modeling.