fsolve with the option newton

10.4.4 fsolve with the option newton_solver

newton_solver is the standard Newton method. The algorithm starts at an initial value x₀, then finds the intersection x₁ of the tangent at x₀ to the graph of f, with the x axis, the next iteration is done with x₁ instead of x₀. The x_i sequence is defined by

x₀=x₀, x_n+1=x_n−

f(x_n)

f′(x_n)

If the Newton method converges, it is a quadratic convergence for roots of multiplicity 1.

Example.
Input:

fsolve((cos(x))=x,x,0,newton_solver)

Output:

0.739085133215