I need to calculate the eigenvector from the highest eigenvalue of an ill-conditioned matrix (kappa > 10^15). Since my goal is not to search for maxima/minima nor to calculate all eigenvectors, I'm not sure whether the ill-condition may be an issue.
Hi, did you already try some numerical routines from MATLAB or FORTRAN to compute this eigenvector ?
Yes. No numerical problem encountered. I tried a second method calculating the same variable (independent from the matrix) and got a similar value.
The question is rather theoretical to ensure further that the result is robust.
Dear Christopher Imanto ,
Your doubts in the ill-conditioned matrices are true.
Hope you find the below articles are helpful to improve your results.
(1)https://pdfs.semanticscholar.org/ada3/1e011982cfce1add6b360ce653e5c47b924b.pdf
(2) link.springer.com/content/pdf/10.1007/BF02165660.pdf
Best regards
Hi, a numerical solution would be to perform the same calculations with a higher precision arithmetic. In FORTRAN for exemple you can switch from DOUBLE PRECISION to REAL*16. The same thing can be possible with other languages. Also with MAPLE or MATHEMATICA it is perhaps possible to obtain the "exact" solution.
I feel you try to compute maximum eigen value and corresponding eigen vector by Power's method. Since the smallest eigen value will be near zero, it will not create any problem in convergence of the procedure.
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix