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Newton's Method Proof

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))

Solution Summary

A Jacobian is employed in this Newton's Method proof. The solution is detailed and well presented.