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Topic: Equations for finding roots


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Subject:   RE: Equations for finding roots
Author: Si
Date: Sep 28 2004
On Sep 27 2004, Rattrap wrote:
> 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 pseudo-codes
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 pseudo-codes, 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 pseudo-codes, 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 (pseudo-codes
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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