Often, there are errors or uncertainties in the data values, , for instance. Perhaps forcing the approximating function to pass through the data points is not the wisest approach.
An alternative approach is to assume a functional form for the unknown f(x) and adjust it to “best fit” the uncertain data. A way to judge what is “best” is needed.
, for instance. Perhaps forcing the approximating function to pass through the data points is not the wisest approach.