Numerical Methods with Programming

Newton's method of solving an equation \(f(x)=0\) is based on iterating a specific function \(g\) such that every root of \(f\) is an attracting (usually super-attracting) point for \(g\text{.}\) The formula for \(g\) is geometrically motivated: it comes from tangent line approximation to the graph of \(f\) and therefore involves its derivative. Since the derivative is not always known, we consider an alternative secant method which replaces the tangent line by a secant line.