Q: Newton-Raphson and Bisection for solving for a system of nonlinear equations? We know that for a single equation root-finding, we can use the Newton's method, or a combination of Newton with bisection to guarantee convergence. Can we use Newton+bisection for a system of nonlinear equations? I can't figure out how bisection could work on multi-dimensional equations.
For example, if Newton iteration causes one equation to have the x-value out of the bisection range, then in the next iteration, does this one equation performs bisection while other equations perform Newton iteration?
