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===Iterative solutions===
Iterative solutions are another method used to solve the problem of error propagation. One example of an iterative solution is a program based on minimizing {{math|{{!}}{{!}}AX−XB{{!}}{{!}}}}. As the program iterates, it will converge on a solution to {{math|X}} independent to the initial robot orientation of {{math|'''R'''<sub>B</sub>}}. Solutions can also be two-step iterative processes, and like simultaneous solutions can also decompose the equations into [[dual quaternion]]s.<ref>Zhiqiang Zhang, et al. [https://link.springer.com/article/10.1007/s11548-017-1646-x "A computationally efficient method for hand–eye calibration."] 19 July 2017.</ref> However, while iterative solutions to the problem are generally simultaneous and accurate, they can be computationally taxing to carry out and may not always converge on the optimal solution.<ref name="tsapps"/>
===The AX=XB case===
The matrix equation {{math|AX{{=}}XB}}, where {{math|X}} is unknown, has an infinitive number of solutions that can be easily studied by a geometrical approach.<ref> Irene Fassi, Giovanni Legnani [https://doi.org/10.1002/rob.20082 "Hand to sensor calibration: A geometrical interpretation of the matrix equation AX =XB."] Journal of Robotic Systems, 28 July 2005</ref>
To find {{math|X}} it is necessary to consider a simultaneus set of 2 equations {{math|A<sub>1</sub>X{{=}}XB<sub>1</sub>}} and {{math|A<sub>2</sub>X{{=}}XB<sub>2</sub>}}; the matrices {{math|A<sub>1</sub>, A<sub>2</sub>, B<sub>1</sub>, B<sub>2</sub>}} have to be dermined by experiments to be performed in an optimized way.
<ref> Giovanni Legnani. [https://doi.org/10.2316/Journal.206.2018.1.206-4974 "Optimization of hand-to-camera calibration using geometrical interpretation of matrix equation AX = XB." ] International Journal of Robotics and Automation - January 2018. </ref>
==References==
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