Numerical Approximation to Roots

[Kreizhn]

Homework Statement

I'm trying to find a root-finding method for a function
[tex] f: \mathbb R^n \to \mathbb R [/itex]

Homework Equations

x is a root of f(x) if f(x) = 0

The Attempt at a Solution

There is lots of work done for this problem when n=1, and also lots of work done when [itex] f: \mathbb R^n \to \mathbb R^n [/itex]. It seems like there should be a Newton method that can be applied here, but it's not entirely obvious to me. I've had some results by using the generalized Moore-Penrose inverse on [itex] \nabla f [/itex] but it's not something I would like to depend on in general. Does anyone know if there's an algorithm for solving this?

 

[mighty2000]

Hello, there are actually several root-finding methods that can be applied to a function of the form f: \mathbb R^n \to \mathbb R. One method that is commonly used is the Newton's method, which involves finding the roots of the derivative of the function. Another method is the Bisection method, which involves dividing the interval where the root is located and narrowing it down until the root is found. Other methods include the Secant method and the Regula-Falsi method. It's important to consider the properties of the function and the desired accuracy when choosing a root-finding method. I would suggest doing some research and experimenting with different methods to find the most suitable one for your specific function. Good luck!