TABLE OF CONTENTS When you are dealing with a sample of experimental data, most often this data is represented in the form of an array composed of pairs of numbers (x i, y i). Subsequently, the problem of approximating discrete dependence y(x i) by using a continuous function f(x) arises. The function f(x), depending on the specific characteristics of the problem, might need to satisfy various requirements:
f(x) must contain all the points (x i, y i), i. e., f(x i)=y i, i=1 n. In this case ( see Section 14.1), we are dealing with data interpolation of the function f(x) in the internal points between x i, or with data extrapolation (outside the interval containing all x i).
f(x) must approximate y(x i) in a specified manner (for example, as a predefined analytical dependence), not necessarily containing all the points with coordinates (x i, y i). In this case, we are dealing with a regression problem ( see Section 14.2), which, in most cases, can be considered to be data smoothing.
f(x) must approximate the experimental dependence y(x i), taking into account some facts, for example, considering that the (x i, y i) data was measured with some error representing the noise component of the measurements.
In this case, the function f(x) uses a specific algorithm to...
