What is the logic behind fzero and fsolve which make fsolve's speed faster than fzero?

What is the logic behind fzero and fsolve which make fsolve's speed faster than fzero? Suppose that there is a polynomial equation, it can be solved by root function in shortest time, following by fsolve and fzero. Why is it so?

Answer 1

[Massimo Zanetti]

The functions fsolve and fzero are not meant to solve the same problem. Specifically:

1. fzero: It finds the root of a function (of one variable) in an interval [a,b]. It REQUIRES that f(a)*f(b)<0. fzeros uses a combination of bisection, secant, and inverse quadratic interpolation methods. Not every polynomial can be rooted by fzero: for instance x^2 doesn't work, because it has no sign change.
2. fsolve: solves a SYSTEM of non-linear equations F(x) where x is multivariate. It use three different methods 'trust-region-dogleg' (default), 'trust-region', and 'levenberg-marquardt', depending on user needs.

[Dariusz Skibicki]

Thank you very much. The only sensible and simple answer. The only thing missing is the fact that fsolve is a Newtonian method.