Variable projection
= Variable projection
= Separable nonlinear least squares
{synonym}
In <variable projection>, a prediction has the form $\mathbf G(\mathbf q)\mathbf m$, nonlinear in $\mathbf q$ but <linear> in $\mathbf m$. For each trial $\mathbf q$, solve the inner <weighted least squares> problem for $\mathbf m$, then optimize the resulting residual over $\mathbf q$. This reduces the nonlinear dimension without pretending that the whole <inverse problem> is <linear>.