Advantages and Disadvantages of Newton's Method
One of the advantages of Newton's method is that its not too complicated in form
and it can be used to solve a variety of problems. The major disadvantage associated
with Newton's method, is that J(x), as well as its inversion has, to be calculated for
each iteration. Calculating both the Jacobian matrix and its inverse can be quite time
consuming depending on the size of your system is. Another problem that we may be
challenged with when using Newton's method is that it may fail to converge. If Newton's
method fails to converge this will result in an oscillation between points.