Editing Levenberg–Marquardt algorithm (section)

==Example==

[[Image:Lev-Mar-poor-fit.png|thumb|Poor fit]]
[[Image:Lev-Mar-better-fit.png|thumb|Better fit]]
[[Image:Lev-Mar-best-fit.png|thumb|Best fit]]

In this example we try to fit the function <math>y = a \cos\left (bX\right ) + b \sin\left (aX\right )</math> using the Levenberg–Marquardt algorithm implemented in [[GNU Octave]] as the ''leasqr'' function. The graphs show progressively better fitting for the parameters <math>a = 100</math>, <math>b = 102</math> used
in the initial curve. Only when the parameters in the last graph are chosen closest to the original, are the curves fitting exactly. This equation
is an example of very sensitive initial conditions for the Levenberg–Marquardt algorithm. One reason for this sensitivity is the existence of multiple minima — the function <math>\cos\left (\beta x\right )</math> has minima at parameter value <math>\hat\beta</math> and <math>\hat\beta + 2n\pi</math>.