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Re: Numerical Determinants


Rod Pinna wrote:
> 
> Hello all,
> 
> I have a large square matrix, of 30x30 elements (and possibly  larger).
> Each element is of the form
> 
>         Ai,j + Bi,j P
> 
> Where Ai,j and Bi,j are real numbers. Evaluation of this matrix  in
> symbolic form is very slow. Obviously, numeric evaluation is  much
> faster. What I want to do is evaluate, with M the matrix  above:
> 
> NSolve[Det[M]==0,P]
> 
> Nsolve seems to, as far as I can tell, first evaluate a symbolic
> expansion of M, rather than numerically substituting numbers. Is  there
> a way to get Mathematica to evaluate this in a purely numeric way?
> 
> I've tried Findroot, but the fuction is badly behaved around the  roots
> of interest, and it doesn't find the roots I'm looking for. Any
> suggestions?
> 
> Thanks,
> Rod Pinna.
> 
> Rod Pinna
> (rpinnaX at XcivilX.uwa.edu.au  Remove the X for email)


My suggestion is to evaluate Det[M] using interpolation. It is a
polynomial in P of degree no larger than 30, so this should be simple.
of the work.


Daniel Lichtblau
Wolfram Research


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