  The objective of this publication is to reduce the sensitivity of iterative
equation solvers on the initial value. To this end, at the hand of Newton's
method, we exemplify how to reformulate the initial problem by means of a set
of generalized moment generating functions. The approach allows to choose that
very function, which is best approximated by a linear function and thus allows
to set up an efficient iteration procedure. As a result of this, the number of
iterations required to meet a given precision goal is significantly reduced in
comparison to Newton's method especially for large deviations between the
initial value and the actual root. At the hand of seven academic examples and
three applications we demonstrate that the computing time of the discussed
approach reveals a far lower susceptibility on the initial value when compared
to results from Newton's method. This insensitivity offers the prospect to
implement iterative equation solvers for applications with strict real-time
requirements such as power system simulation or on-demand control algorithms on
embedded systems with low computing power. We are confident that the devised
methodology may be generalized to other well-established iteration algorithms.
