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At a minimum of the sum of squares ''S'', we have ∇<sub>'''q'''</sub>''S''=0. With the above linearization, this leads to the following equation
:('''J'''<sup>T</sup>'''J''')'''q''' = -2'''J'''<sup>T</sup>'''f'''
from which '''q''' can be obtained by inverting '''J'''<sup>T</sup>'''J'''.
The key to the LMA is to replace this equation by a 'damped version'
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