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defunc
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Are there any variations of Newtons method, say where you use higher derivatives?
HallsofIvy said:We could, as well, approximate the function by a parabola that (1) passes through the given point, (2) has the same slope their, and (3) has the same second derivative.
defunc said:Are there any variations of Newtons method, say where you use higher derivatives?
Newton's method is an iterative algorithm used to approximate the roots of a function. It is based on the idea of using tangent lines to approximate the roots of a function.
Some variations of Newton's method include the modified Newton's method, the quasi-Newton method, and the damped Newton's method. These variations aim to improve the convergence and stability of the original Newton's method.
The modified Newton's method, also known as the secant method, uses secant lines instead of tangent lines to approximate the roots of a function. This can sometimes improve the convergence rate of the method.
The quasi-Newton method is a generalization of Newton's method that uses an approximation of the Hessian matrix instead of calculating it directly. This can be more computationally efficient for functions with a high number of variables.
The damped Newton's method adds a damping factor to the Newton's method iteration in order to improve the stability of the algorithm. This can prevent overshooting and oscillations that may occur in the original Newton's method.