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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'
:('''J'''<sup>T</sup>'''J''' + λ'''I''')'''q''' = -'''J'''<sup>T</sup>'''f'''.
The (non-negative) damping factor λ is adjusted at each iteration. If reduction of S is rapid a smaller value can be used bringing the algorithm closer to the GNA, whereas if an iteration gives insufficient reduction in the residual λ can be increased giving a step closer to the gradient descent direction. A similar damping factor appears in [[Tikhonov regularization]], which is used to solve linear ill-posed problems.
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