The secant method of root-finding does not pose divergence problems.

Question

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The secant method may pose convergence problems if the initial interval for the search does not contain the root, or if the function has a flat slope or behaves nonlinearly in the vicinity of the root. In such cases, the iterations may fail to converge or oscillate around the root. The secant method of root-finding can pose divergence problems if the starting points are not chosen carefully or if the function being evaluated has multiple roots or sharp curves. This is because the secant method is a quasi-linear method that relies on linear approximations of the function and can diverge if the approximations are poor.

The Secant Method of Root-Finding Does Not Pose Divergence Problems