assuming a solution exists, one gives conditions such that iterates chosen sufficiently close to that solution converge to that solution.
A note on inexact secant methods
Abstract The inexact secant method \([x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k\), \( x_{k+1}=x_k+s_k\), \( k=1,2,\ldots\), \( x_0,x_1 \in {\mathbb R}^n\) is considered for solving the nonlinear…