Re: Roots of polynomials

[Stephen Montgomery-Smith]

If you know the real part of the root of p(z), call it s, you could try
using fzero on the function
f1(t) = p(s+I*t)
Or since it is unlikely that you know s exactly, you could use fmin (in
the optim package) to miminize abs(p(s+I*t)).


On 04/17/2013 06:56 AM, Urs Hackstein wrote:
> But how can such a direct search along the imaginary part of the root be
> done? I tried to compute the integral \int_\alpha (f'/f )s over a curve
> \alpha surrounding the root, but this is still slower than the roots
> routine.
> 
> 
> 2013/4/17 Benjamin Abbott <address@hidden <mailto:address@hidden>>
> 
>     On Apr 17, 2013, at 6:49 AM, Urs Hackstein
>     <address@hidden <mailto:address@hidden>>
>     wrote:
> 
>     > Hello,
>     >
>     > there exists a built-in function "roots" which computes the roots
>     of a given polynomial. How does octave computes these roots? This
>     function is pretty fast, but are there faster functions doing the
>     same? We have to compute the roots of a huge number of polynomials
>     in our program, thus this could minimize the runtime.
>     >
>     > Or are there faster algorithms in the case that we aren't
>     interested in all roots, but only in a special root whose real part
>     is already known?
> 
>     The roots are found by constructing a matrix whose characteristic
>     polynomial is a scaled version of the polynomial in question.
> 
>     The eigen values of that matrix are the roots of the polynomial.
> 
>     For the general case, this is the fastest approach.  For your case a
>     direct search along the imaginary part of the root may be faster.
> 
>     Ben
> 
>