ABSTRACT
This chapter considers one of the most encountered problems in scientific computing, which is the problem of computing the root or zero of a real valued function of one variable. It focuses on three basic methods: the bisection, Newton’s and the secant methods. In short, any of these methods compute a solution of a nonlinear equation starting from one initial data, then adopting some iterative method that, under favorable conditions, will converge to a zero of the function. The bisection method is a procedure that repeatedly “halves” the interval in which a root has been located. The Newton’s method is one of the most powerful numerical methods for solving non-linear equations. It is also referred to as the tangent method. The chapter also provides a comparison between the convergence of both the Newton and secant methods.
