How to prove newton's method?
As above. Thanks
As above. Thanks
1 Answer
# x_(n+1) = x_n - f(x_n)/(f'(x_n)) #
Explanation:
Suppose we seek a solution to the equation:
# f(x) = 0 #
And that we have an initial estimate
The tangent to the curve at he point
# y - f(x_0) = f'(x_0)(x-x_0) #
The point
# 0 - f(x_0) = f'(x_0)(x_1-x_0) #
And if we rearrange for
# :. f'(x_0)(x_1-x_0) = -f(x_0) #
# :. x_1-x_0 = -f(x_0)/(f'(x_0)) #
# :. x_1 = x_0 - f(x_0)/(f'(x_0)) #
Leading to the general Newton's Method iterative method:
# x_(n+1) = x_n - f(x_n)/(f'(x_n)) #