## A sufficiently exact inexact Newton step based on reusing matrix information

Newton’s method is a classical method for solving a nonlinear equation \$F(z)=0\$. We derive inexact Newton steps that lead to an inexact Newton method, applicable near a solution. The method is based on solving for a particular \$F'(z_{k’})\$ during \$p\$ consecutive iterations \$k=k’,k’+1,\dots,k’+p-1\$. One such \$p\$-cycle requires \$2^p-1\$ solves with the matrix \$F'(z_{k’})\$. If matrix … Read more