= Non-linear least squares
{title2=$f(x)=\tfrac12\|R(x)\|_2^2$}
{wiki}
= Nonlinear least squares
{synonym}
Here the residual map $R$ may be nonlinear. Its <Jacobian matrix> $J=DR$ gives $\nabla f=J^TR$ and $\nabla^2f=J^TJ+\sum_jR_j\nabla^2R_j$. The <Gauss-Newton algorithm> drops the second term to obtain an approximation using only first derivatives of the residuals. Full column rank of $J$ makes $J^TJ$ positive definite; at a zero-residual solution this approximation equals the exact Hessian.
Back to article page
