Two methods for co nstructing solutions to t he problem of minimizing an integral in a certain class of arcs joining a pair of fixed points are proposed. One of t hese procedures is a generalization of Newton's method, while the other is a "gradient" method. Co ndition s for convergence to a strong r elat iv e mi nimum are given in both cases.
A division problem is defined and notation to relate it to the problem of multiple precision operation in a digital computer is introduced. A basic divide-and-correct method for multiple precision division is formulated and its known properties briefly reviewed. Of particular interest is the fact that the method produces at each step a set of precisely three estimates for the desired result, one of which is exact.
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