The objective of this work was to develop new algotithms for solving
systems of equations by combining three different methods; the method of
gradient descent (GV), a modified method of gradient descent (MGV) und
Newton's methode (NV). As iterative methods all of the above calculate a
new point of the iteration through a sum of the old point and an adjustment
until they find the solution of the problem. By combining these adjustments
in each step of the iteration we will create new algorithms. For linear
systems of equations we will combine the GV the MGV and the NV. For
nonlinear systems of equations a combination of two different NV's ans the
MGV will be analysed. The algorithms were implemented in the CAS Maple and
tested on many examples of low dimension.