Please show that when n=1, Newtons method given by:
x^k=x^(k-1)-(J(x^(k-1))^-1)(F(x^(k-1)) for k>=1
reduces to the familiar Newton's method given by:
P_n=P_n-1 - f(p_n-1)/f'(P_n-1) for n>=1
^-1 is inverse
J is the jacobian matrix
The top equation is called newton's method for non linear systems. x is a vector. F(x_1,...,x_n)=(f_1(x_1,...,x_n),f_2(x_1,...,x_n),...,f_n(x_1,...,x_n)).
A Jacobian is employed in this Newton's Method proof. The solution is detailed and well presented.