Broyden's method belongs to a family of methods that are like this one, but use an approximate Hessian or Jacobian. This method precedes Halley's method as the first of Householder's methods, and shows (*) quadratic convergence for close starting points. In this method, each iterate is produced by subtracting from the previous iterate the quotient of the function and its derivative, both evaluated at that iterate. For 10 
Broyden's method belongs to a family of methods that are like this one, but use an approximate Hessian or Jacobian. This method precedes Halley's method as the first of Householder's methods, and shows (*) quadratic convergence for close starting points. In this method, each iterate is produced by subtracting from the previous iterate the quotient of the function and its derivative, both evaluated at that iterate. For 10 points, name this method that uses the x-intercepts of tangent lines to approximate the roots of a function.
Broyden's method belongs to a family of methods that are like this one, but use an approximate Hessian or Jacobian.
Newton-Raphson method [or Newton's method]