Optimally Controlled Iterative Schemes For Obtaining Solution Of A Nonlinear Equation

An approach is presented for designing a recursive algorithm for finding the root or roots of the equation ƒ(x) = 0, where ƒ is a continuously differentiable function from Rn → Rn . A differential equation, or difference equation, is written with ƒ as the dependent variable and a control vector u as the forcing function. Optimal control theory is then used to drive ƒ from a given initial value to zero.