Question: Huge MATLAB/Maple Discepency

First of all, is there a way I could add maple and matlab scirpts on this forum to make my questions more readable ?? I know we can enter latex scripts on a lot of the latex forums and it's very convenient.


I have a matrix that's a function of a few parameters.  I evaluate this matrix at specified values of those parameters and Maple gives me:

-10123.5740   14316.89761    5065.657044

14316.89761  -20246.81544   3581.960447

5065.657044  3581.960447    0.335338

While Matlab gives me: (x10^4)

  -1.012357539219784   1.431689761935272   0.506565704398669
   1.621994295553999  -2.024681544639569   0.358196044696839
   0.506565704398669   0.358196044696839   0.000033533800000

Already there's some discrepency: element (2,2) ends in 44 in Maple and 45 in Matlab.

1: Does anyone know where I can find out which algorithm Maple and Matlab use for rational function evaluation ?? I'd like to know which one is more accurate.

2: Can I get Maple (or Matlab) to use a better algorithm for rational function evaluation ?? Or truncate less digits during intermediate steps ??


Ok so I can live with the matrix being different.  Now for the eigenvalues:




  1.0e+004 *



This I cannot live with.  And neither can the astronaut on his way to Mars taking  my calculations for granted.


Matlab's eigenvalues match pretty well with the eigenvalues that my FORTRAN code spits out (my FORTRAN code uses Jacobi rotations, which can theoretically be arbitrarily accurate given enough iterations). 

How do I find out what algorithm Maple (and Matlab) use for eigenvalues.  And how do I get it to use a more accurate algorithm ?? Or truncate less digits during intermediate steps ????

Any help is GREATLY appreciated






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