These are all methods used to find the root of an equation f(x) = 0. That is to say, they find one or more values of x for which the function of x is equal to zero.

Another common characteristic is that they take one or more initial "guesstimates" of the root, and use a number of recursive functions to calculate new values of the root, with ever increasing accuracy. That is, if it works right. Some of them don't work in all situations. Some of them hardly work in any. Oh well. That should be covered in the individual write-ups. Anyways, here's a little list.

These methods aren't perfect. They usually won't get you the exact value of the root. But, as long as you keep doing the iterations long enough, they should get more and more accurate. Honestly, do you really need to be accurate to more than 7 decimal places for anything anyways?

Some of them won't always work. For example, the bisection method will totally not work if the function only touches the x-axis, instead of crossing it. Some will take a long time to work. Although some can also be sped up, if you know how. I don't. Some might only work depending on if you pick your initial guesses closely enough. Others just involve a whole lot of calculations. Pick the method depending on exactly what you need to find.

If you have a function that is easily differentiable, use the Newton-Raphson method. If want to make SURE that you will find a point where the function crosses the x-axis, try the bisection method. If you need to find the values of complex roots, use Müller's or Bairstow's method. They each have their flaws, and their strengths. Choose wisely.

One thing that they do all have going for them, is the fact that because they are iterative, they are quite suited for use by computer programs, using do while loops and stuff like that.

Oh, and if I missed any, /msg me.

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