Category talk:Root-finding algorithms

Why is the definition of root-finding algorithms restricted to the case where x is scalar? Newton's method can also be used to find zeros of vector functions. I also don't understand why root-finding algorithms should be a subcategory of optimization algorithms. None of the root-finding algorithms is in common use in optimization, as far as I know. -- Jitse Niesen 19:49, 25 Jun 2004 (UTC)

That's the definition of a root --- a scalar where a scalar-valued function reaches zero. Root-finding is much much easier than general non-linear equation solving. See, e.g., [1] Newton's method is both a root-finding algorithm and an optimization algorithm, depending on which version of Newton's method is used. The article Newton's method focuses almost exclusively on the scalar version, so it seemed like it belongs here.

Root finding can be considered a form of optimization. If you apply root-finding to f'(x) = 0, where f is scalar-valued and x is a scalar, then you find the extremal points of f(x). But, this is not a strong association. If you'd like to move root-finding back to Category:Numerical analysis, I wouldn't be upset.

-- hike395 01:50, 26 Jun 2004 (UTC)