Root finding methods for Polynomials.

[mhill]

Hi , is there a method to obtain the roots of Polynomials:

$$P(x)=a_{0}+a_{1}x+a{2}x^{2}+...+a_{n}x^{n}$$

i know there are , but my problem is this if we knew that are complex roots of the form z=a+ib , would be a method to obtain the complex root with BIGGER and SMALLER real part ?? , i mean for example if a POlynomial has complex root:

1+3i 1-3i 0.6+8i 0.6-8i 0.01+34i 0.01-34i ...

my question is if we could use a root finding algorithm to check that the bigger part of the roots is '1'

 

[John Creighto]

I'm not sure what you mean. Matlab has a good method for finding the roots numerically. It transfers the roots of polynomial to an eigvenvalue problem. It converges quite fast and will give you all the roots. It is quite accurate if the eignvalues are well separated.

 

[coomast]

One method to find all roots is the one of Bairstow. This gives you not only the real, but also the complex ones. Look here for some info, and google a bit to find some more:

http://en.wikipedia.org/wiki/Bairstow's_method

The implementation is not that difficult, I've done it and it works fine. The only thing to take care of is a good starting value, but even that can be solved.