Newton's method

In math, Newton's method (also known as the Newton–Raphson method, named after Sir Isaac Newton and Joseph Raphson) is a method for finding the zeroes (or roots) of a function whose values are all real. Newton's method often converges very quickly, especially if the "guess value" begins sufficiently near the desired root. Just how close "sufficiently near" needs to be, and just how fast "remarkably quickly" can be, depends on the problem. Unfortunately, when the initial guess is far from the root, Newton's method can lead an unwary user astray with little warning.