secant method

Therefore, the secant method may occasionally be faster in practice.

It is a generalization to the secant method for a multidimensional problem.

The method is a generalization of the secant method.

The first one is given by linear interpolation, also known as the secant method:

He inserted an additional test which must be satisfied before the result of the secant method is accepted as the next iterate.

The order of this convergence is approximately 1.8, it can be proved by the Secant Method analysis.

If the initial values are not close enough to the root, then there is no guarantee that the secant method converges.

In one dimension, solving for and applying the Newton's step with the updated value is equivalent to the secant method.

A generalization of the secant method in higher dimensions is Broyden's method.

Replacing the derivative in Newton's method with a finite difference, we get the secant method.

The secant method also arises if one approximates the unknown function f by linear interpolation.

It converges faster than the secant method.

In the secant method, we replace the first derivative with the finite difference approximation:

The idea to combine the bisection method with the secant method goes back to .

If applied iteratively, either the secant method or the improved formula will always converge to the correct solution.

Using linear interpolation instead of quadratic interpolation gives the secant method.

Using this approximation would result in something like the secant method whose convergence is slower than that of Newton's method.

The false position method (or regula falsi) uses the same formula as the secant method.

The false position method, also called the regula falsi method, is like the secant method.

Quasi-Newton methods are a generalization of the secant method to find the root of the first derivative for multidimensional problems.

Both the secant method and the improved formula rely on initial guesses for IRR.

In numerical analysis, double false position became a root-finding algorithm that combines features from the bisection method and the secant method.

Given two estimates and for IRR, the secant method equation (see above) with will always produce an improved estimate .

Like the secant method, it is an iterative method which requires one evaluation of in each iteration and no derivatives of .

The iterates of the secant method converge to a root of , if the initial values and are sufficiently close to the root.