Given a sufficiently smooth vector-valued function r(x), a local minimizer of ‖r(x)‖2 within a closed, non-empty, convex set F is sought by modelling ‖r(x)‖q2/q with a p-th order Taylorseries approximation plus a (p + 1)-st order regularization term for given even p and some appropriate associated q. The resulting algorithm is guaranteed to find a value x̄ for which ‖r(x̄)‖2 ≤ ǫp or χ(x̄) ≤ ǫd, fo...

When the exact time-dependent solutions of a system of ordinary differential equations are chaotic, numerical solutions obtained by using particular schemes for approximating time derivatives by finite differences, with particular values of the time increment τ , are sometimes stably periodic. It is suggested that this phenomenon be called computational periodicity. A particular system of three...