ABSTRACT
In the preceding chapter, we derive equations which fit a given of data either exactly, or, by using a criterion such as the least-squares method. Once such equations have been obtained in the form of y = C(x) when the data are two-dimensional, or, z = S(x,y) when the data are three-dimensional. It is next of common interest to find where the curve C(x) intercepts the x-axis, or, where the surface S(x,y) intercepts with the x-y plane. Mathematically, these are the problems of finding the roots of the equations C(x) = 0 and S(x,y) = 0, respectively. The equation to be solved could be a polynomial of the form P(x) = a1 + a2x + … + aixi−1 + … + aN +1 XN which is of Nth order, or, a transcendental equation such as C(x) = a1sinx + a2sin2x + a3sin3x.
