Mit18 330 s12_chapter4

This document discusses three methods for finding the roots of nonlinear equations: 1) Bisection method, which converges linearly but is guaranteed to find a root. 2) Newton's method, which converges quadratically (much faster) but may diverge if the starting point is too far from the root. 3) Secant method, which is faster than bisection but slower than Newton's, and also requires starting points close to the root. Newton's and secant methods can be extended to systems of nonlinear equations.