What is the mathematical technique called that estimates an unknown value from surrounding values?

The technique referred to is commonly known as interpolation. This method involves estimating an unknown value that lies within the range of known values. In the context of data analysis, interpolation is often used to predict values at positions within a set of data points. For instance, if you have two data points (e.g., measurements at certain times), interpolation allows you to estimate the value at a time that falls between those two points.

Interpolation relies on the understanding that the values of a function are closely related to their adjacent values, making it an ideal choice when you have a limited dataset and wish to fill in gaps. This is especially relevant in fields like imaging, where pixel values in a grid can be estimated based on surrounding pixels to enhance image resolution or create smoother transitions.

In contrast, extrapolation extends beyond the range of known values to estimate unknown values, which can be less reliable due to the assumptions involved in extending trends. Estimation is a more general term that encompasses various techniques for approximating values. Regression analysis involves modeling the relationship between variables and making predictions based on that model, which is a more complex approach to data analysis than simple interpolation.