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.
Menini, L., Possieri, C., Tornambe', A. (2023). Design of higher order iteration maps for multi-variable polynomials via algebraic geometry. In IFAC-PapersOnLine (pp.7246-7251). Elsevier B.V. [10.1016/j.ifacol.2023.10.333].
Design of higher order iteration maps for multi-variable polynomials via algebraic geometry
Menini L.;Possieri C.
;Tornambe' A.
2023-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
