ABSTRACT
In this chapter, the authors discuss one of the oldest approximation problems which consists of finding the roots of an equation. It is also one of the most commonly occurring problems in applied mathematics. Although the bisection method always converges and is easy to program, compared to other methods, its rate of convergence is rather slow. Newton’s method is one of the most widely used of all iterative techniques for solving equations. MATLAB contains two commands to compute the roots of functions. The first command, roots, is specifically written to find the roots of a polynomial. The second command, fzero, is designed to find the roots of f(x) provided the function actually crosses the x-axis at the root. Starting with an initial estimate of the solution, Newton’s method consists of approximating each nonlinear function by its tangent plane; and the common root of the resulting linear equations provides the next approximation.
