Discussion:  All Topics 
Topic:  Equations for finding roots 
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Subject:  RE: Equations for finding roots 
Author:  Si 
Date:  Sep 28 2004 
> I'm working on some 3d software, and am currently working on trying
> to use some of the SIMD CPU functions (MMX,SSE,3DNow,etc). I have
> been trying to find the mathematical equations or processes for
> computing the nth root of a number, with no real luck yet.
For general roots (involving Real & Complex roots), use the De Moivres
formulas.
There is an applet here for complex numbers that also show how to find Nth root
of any number (Real & Complex). WARNING  be patient as it takes long for the
applet to load.
http://mathforum.org/te/exchange/hosted/palu/complexnumber/ComplexNumbers.html
If you want to analyze only real roots of numbers and one variable functions,
then get a good book on numerical analysis, where they will show pseudocodes
of how to write such routines for different problems. One of the popular books
and also a standard text for scientific computing courses at University level in
Maths, Physics, Engineering which is called:
Title  "Numerical Analysis" (7th Ed)
Authors  "R.L Burden & J.D.Faires"
Publisher  "Brooks/Cole"
You will find in chapter 2 which cover "root findings" of expressions in one
variable. Algorithms are listed in pseudocodes, which you can code it
directly in any computer language , even if you do not understand the maths (or
its derivation). That is the beauty of pseudocodes, which tells you how to
code a mathematical procedure without even understanding how it is solved. I
know some coders (programmers) who use numerical analysis books to learn in a
back to front manner. This means they understand the procedures (pseudocodes
algorithms) well when coding them in any computer language, they then try and
learn what the codes mean in mathematical theory.
Cheers,
Sione.
 
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