I was eleven years old when I first saw Newton's method. No, I didn't go to a school for geniuses. I didn't even know it was Newton's method until decades later. However, in sixth grade I learned an iterative algorithm that taught me (almost) everything I need to know about
Statistical programmers often need to evaluate complicated expressions that contain square roots, logarithms, and other functions whose domain is restricted. Similarly, you might need to evaluate a rational expression in which the denominator of the expression can be zero. In these cases, it is important to avoid evaluating a function
In my article about finding an initial guess for root-finding algorithms, I stated that Newton's root-finding method "might not converge or might converge to a root that is far away from the root that you wanted to find." A reader wanted more information about that statement. I have previously shown
