Concept solve 𝐽𝑇(𝑥𝑘)𝐽(𝑥𝑘)𝑠𝑘=−𝐽𝑇(𝑥𝑘)𝑟(𝑥𝑘) ⟹𝐽(𝑥𝑘)𝑠𝑘=−𝑟(𝑥𝑘) instead of 𝐻𝑓(𝑥𝑘)𝑠𝑘=−∇𝑓(𝑥𝑘) in Newton’s method. It like Newton’s method applied to truncated Hessian matrix.