Newton system ($DF(x)\delta =-F(x)$)

The linear system defining one step of Newton's method for $F(x)=0$ is the displayed first-order correction equation. A nonsingular Jacobian matrix gives a unique Newton correction. For an unconstrained stationary-point problem $F=\nabla f$, the system uses the Hessian matrix in place of $DF$.

The correction is the vector obtained by solving the Newton system, added to the current point to give $x_{\mathrm{new}}=x+\delta$. The inverse notation specifies the solution; a numerical implementation normally solves a linear system rather than forming a matrix inverse.