Finally, Steepest Descent simply assumes 𝛁𝛁𝛁𝛁𝛁𝛁 = 𝟙𝟙. The advantage of the Gauss-Newton algorithm over Newton is time saved in not computing 𝐇𝐇, which is usually quite significant. Newton is also susceptible to convergence problems far from the global minimum, unlike the other algorithms mentioned. The Gauss-Newton approximation is often justified because near the global minimum the residual 𝐫𝐫 is relatively small and mostly random with zero mean, implying 𝐇𝐇 is negligible. The Levenberg-Marquardt algorithm interpolates between the limiting cases of Gauss-Newton (𝜆𝜆 → 0) and Steepest Descent (𝜆𝜆 → ∞). The advantage of Levenberg-Marquardt is the added stability of inverting 𝛁𝛁𝛁𝛁𝛁𝛁 due to the λ𝟙𝟙 term, however, this is irrelevant in our case as our algorithm guards against singular 𝛁𝛁𝛁𝛁𝛁𝛁 (Section C below). The disadvantage of Levenberg-Marquardt is that successful optimization for λ is difficult to predict and usually requires a dynamic routine. Furthermore, as λ increases, Levenberg-Marquardt behaves more like Steepest Descent which is slower to converge near minima because 𝛁𝛁𝛁𝛁𝛁𝛁 → λ𝟙𝟙 ignores the true curvature of C(𝐩𝐩). Therefore, we have chosen the Gauss-Newton approximation in Eq. 5.