= Newton step
{c}
{title2=$H(p)s=-\nabla f(p)$}
A Newton step for <Newton's method in optimization> is the <displacement> $s$ solving the displayed <linear system>, where $H$ is the <Hessian matrix> and $\nabla f$ the <gradient>. The next iterate is $p+s$. This makes the first order <Taylor expansion> of the <gradient> at the new point vanish. An invertible <Hessian matrix> determines a unique step; it need not give a descent direction when the <Hessian matrix> is indefinite.
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