Generalized bisection methods for imprecise problems

Efficient numerical methods for locating and computing to any desired accuracy solutions of systems of nonlinear algebraic and transcendental equations of the form F-n(x) = O-n with F-n = (f(1),...,f(n)):(D) over bar subset of IR(n) --> IR(n), are described. The methods presented here are based on the nonzero value of the topological degree of the function F-n at O-n relative to D and are particularly useful since the only computable information required is the algebraic signs of the components of the function. Our methods always converge rapidly to a solution independently of the initial guess and are particularly efficient when the system has many solutions close to each other, all of which are desired for the application.