Selection of interpolation and fitting

Interpolation requires curves and surfaces to pass through data points accurately, while fitting means that curves and surfaces approach (generally do not pass through) data points. Let's take the curve as an example to illustrate the difference between them.

Example 1:

If there are 10 plane points, each point can be accurately passed by a polynomial curve of degree 9, which is an interpolation method;

Example 2:

If there are 10 plane points, these points can be approximated by a quadratic polynomial curve, which is a fitting method;

Example 3:

If there are 100 plane points, there are two methods to require a curve to pass through these points approximately: interpolation and fitting.

We may prefer to use quadratic, cubic or "low" polynomial curves instead of 99-degree curves for interpolation. In other words, this interpolation curve only passes through three or four points (or a group of sparse data points), which involves "filtering" or other mathematical methods, that is, filtering out more than 90 unnecessary points.

If fitting is used, taking least square fitting as an example, we can find a (or several segmented) low-order curve (the number of times is specified by ourselves) to approximate these data points. For specific methods, please refer to the overdetermined equation in solving linear equations in numerical analysis.

Simply put, interpolation is an accurate process and fitting is an approximation.

Look at/question/264115147.html.