An iterative equation solver with low sensitivity on the initial value

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.