Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determinant of Characterisitic Polynomial

  1. Jan 24, 2014 #1
    I'm doing a calculation which finds the characteristic polynomial of a matrix, HH, with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 it finishes evaluating the Discriminant command within a few hours, but at a 10x10, which is what I need, it takes days to evaluate. Running in parallel won't work for the built in Discriminant command. I was wondering if there was a more efficient way to evaluate the discriminant of high-order polynomial, as I know my code is basic.

    CPHH = Collect[CharacteristicPolynomial[HH, x],x]];
    DD = Discriminant[CPHH, x, Method -> SylvesterMatrix];
    Simplify[DD, TimeConstraint -> Infinity]

    If the rest of the code would be useful in determining a solution I'd be happy to post it

    ***Meant Discriminant in Title***
     
  2. jcsd
  3. Jan 24, 2014 #2
    Well, I have not had to do Matlab nor linear algebra since grad school (a couple of decades ago), so, I had to look up what Characteristic Polynomial is...I just saw a video in YouTube where the prof solved the Char. Poly for a 3x3 matrix in a few minutes....does it really take a few hours to solve a 7x7 in matlab?...I feel like I could solve it by hand in less than one!

    What do you mean by "rather complex entries"?

    Back then, matlab was not faster than a C or Fortran program; lately, I have seen postings in forums that seem to indicate that that continues to be the case...maybe you should write your own program to solve this.
     
  4. Jan 24, 2014 #3
    Finding the characteristic polynomial takes seconds in mathematica. Its evaluating the discriminant of that polynomial that takes so long.

    A typical entry in the 21x21 looks like this 1/2 h (61 h k1 - 159 h k2 - 14 g Hz uB). I forgot the particle is spin 10 so the hamiltonian is 21x21, not 10x10 like I said earlier.

    Unfortunately it's required of me to use mathematica, as that is what everyone in the research group uses.
     
  5. Jan 24, 2014 #4
    Oh, so it is mathematica and not matlab...same problem, I don't use either.

    I looked up Discriminant of a Polynomial, now...I see that they can get pretty lengthy and you seem to be using non-numeric entries which I presume makes things more time consuming.

    Anyway, good luck, I am afraid I can't help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determinant of Characterisitic Polynomial
Loading...