Concept

𝑥𝑘+1=𝑥𝑘𝐻1𝑓(𝑥𝑘)𝑓(𝑥𝑘)

where 𝐻 is Hessian matrix and is gradient.
For the 𝐻1 here, we can solve it instead of inverting like we did in chapter 5:

𝐻𝑓(𝑥𝑘)𝑠𝑘=𝑓(𝑥𝑘)

and

𝑥{𝑘+1}=𝑥𝑘+𝑠𝑘

Cost

it has quadratic convergence rate.

Variants