Abstract
In this paper, algorithmic procedures based on algebraic geometry tools are proposed to design iteration maps with arbitrary order of superlinear convergence, for the solution of systems of multi-variable polynomial equations. First, the design is carried out in the single-variable case to illustrate its properties and to highlight its relation with the celebrated Newton and Householder iterative methods. Secondly, the proposed techniques are extended to the multi-variable case. The effectiveness of the proposed approach is highlighted via its application to the inverse kinematics of a robot arm.
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