(8) |
Linearization implies that we approximate this equation with one in which we neglect all terms containing x raised to a power m>1 (x^{2}, x^{3}, etc.) (c.f. Introduction). In this example, linearization reduces the equation to:
f(x) = 1 - x | (9) |
The root of the linearized equation f(x)=1-x=0
is 1, which provides a reasonable initial guess for the actual roots on
the nonlinear equation, in the absence of a plot such as Figure 1.