ABSTRACT
This chapter considers root finding algorithms. It presents the general strategy and several classic algorithms: bisection, false position, Newton–Raphson, and Ridders. The chapter discusses potential pitfalls of numerical methods and review advantages and disadvantages of the classic algorithms. It shows that how matrix laboratory built-in methods are used to find the root of an equation. Broadly speaking, all methods presented in this chapter are of the trial and error type. One could attempt to obtain the solution by just guessing it, and eventually, one would succeed. Each guess can provide some clues that would point us in the right direction. The main difference between algorithms is in how the next guess is formed. The Newton–Raphson method also approximates the function with a line. The non-bracketing algorithms, such as Newton–Raphson and secant, usually converge faster than their bracketing counterparts.
