Differential Equations and Linear Algebra, 4th Edition

3.7 Linear Equations and Curve Fitting

Linear Equations and Curve FittingLinear algebra has important applications to the common scientific problem of representing empirical data by means of equations or functions of specified types. We give here only a brief introduction to this extensive subject.

Typically, we begin with a collection of given data points $(x_0,y_0),(x_1,y_1),\dots ,(x_n,y_n)$ that are to be represented by a specific type of function $y=f(x).$ For instance, y might be the volume of a sample of gas when its temperature is x. Thus the given data points are the results of experiment or measurement, and we want to determine the curve $y=f(x)$ in the xy-plane so that it passes through each of these points; see Figure 3.7.1. Thus we speak of “fitting” ...