[Date Index]
[Thread Index]
[Author Index]
Re: Problems with NSolve
*To*: mathgroup at smc.vnet.net
*Subject*: [mg88167] Re: [mg88144] Problems with NSolve
*From*: Carl Woll <carlw at wolfram.com>
*Date*: Sun, 27 Apr 2008 04:57:11 -0400 (EDT)
*References*: <200804260743.DAA08637@smc.vnet.net>
kgwagh at gmail.com wrote:
>Hi all
>
>I am trying to find the number of eigenvalue crossings for a matrix as
>a function of the parameter 'u', on which the elements of the
>(symmetric) matrix depend on linearly. The matrix elements also
>involve randomly chosen constants. The plan is to find the
>distribution of the crossings of these type of matrices as I scan over
>the random numbers.
>
>So far I have been using the following :
>
>NSolve[{chpoly[u, dim, \[Alpha], \[Gamma], \[Epsilon], x] == 0,
> D[chpoly[u, dim, \[Alpha], \[Gamma], \[Epsilon], x], x] == 0}, {x,
> u}, WorkingPrecision -> prec]
>
>where chpoly is the characteristic polynomial of the matrix (with the
>eigenvalue variable being x) and \alpha, \gamma and \epsilon are
>constant parameter arrays of random numbers. For a double (or higher)
>degeneracy of the eigenvalues both the characteristic equation and its
>derivative should be zero. This approach has worked successfully only
>upto 12*12 matrices (where one such computation takes 40 secs on my
>laptop). For 13*13 my laptop takes 4000 sec. This seems to be somewhat
>surprising, because these polynomials are of the order 'n' (where n
>is dimension of the matrix) in both u and x - and n=13 does not sound
>very computationally unreasonable. So I was wondering if there was a
>faster approach I could take.
>
>Also, the problem essentially entails me to know the number (not the
>values) of the real solutions to this system of polynomials.
>CountRoots seemed ideal but it does not work for more than one
>equation. So is there any alternative along this route?
>
>Any other alternatives are also welcome.
>Thanks,
>Kshitij.
>
>
I would find it helpful if you specified what chpoly, \[Alpha] etc were
to help diagnose you're problem. However, it seems you are coming across
an issue described in the following thread:
http://tinyurl.com/53cp5u
I believe there are other threads that discuss this issue as well, but I
couldn't find them in a quick search.
Carl Woll
Wolfram Research
Prev by Date:
**Re: Problems with NSolve**
Next by Date:
**Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)**
Previous by thread:
**Problems with NSolve**
Next by thread:
**Re: Problems with NSolve**
| |