The root of a function f(x) (f:R → R) is simply some
value r for which the function is zero, that is,
f(r) = 0.
This topic is broken into two major sub-problems:
- Finding the root of a real-valued function of a single variable, and
- Finding the root of a vector-valued function of a many variables.
There are five techniques which may be used to
find the root of a univariate (single variable) function:
- Bisection method
- False-position method
- Newton's method
- Secant method
- Müller's method
Given a vector-valued multivariate function f(x) (f:Rn → Rn), we will
focus on a generalization of Newton's method to find
a vector of values r such that each of the
functions is zero, that is, f(r) = 0.