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I'm calculating eigenvalues of a matrix, [[2,-1,0],[-1,2,-1],[0,-1,2]].
In CAS with eigenvals() I get √2+2, 2, 2-√2, ok
With EIGENVAL() I get "Low accuracy" warning, then Bad Argument Value (like in Home)...

What's the problem?
Thank you

Salvo
(06-02-2015 09:50 PM)salvomic Wrote: [ -> ]I'm calculating eigenvalues of a matrix, [[2,-1,0],[-1,2,-1],[0,-1,2]].
In CAS with eigenvals() I get √2+2, 2, 2-√2, ok
With EIGENVAL() I get "Low accuracy" warning, then Bad Argument Value (like in Home)...

Salvo

I get the same error !!!
Very interesting, you have found an example of matrix that enter an infinite loop when applying Francis numeric algorithm with 2 real shifts (the loop is infinite because the matrix is already in Hessenberg form and the shifts are exact integers). Introducing a small rounding error breaks the infinite loop, I'm updating the giac source code to do that.
(06-03-2015 06:24 PM)parisse Wrote: [ -> ]Very interesting, you have found an example of matrix that enter an infinite loop when applying Francis numeric algorithm with 2 real shifts (the loop is infinite because the matrix is already in Hessenberg form and the shifts are exact integers). Introducing a small rounding error breaks the infinite loop, I'm updating the giac source code to do that.

thank you!
(06-02-2015 09:50 PM)salvomic Wrote: [ -> ]I'm calculating eigenvalues of a matrix, [[2,-1,0],[-1,2,-1],[0,-1,2]].
In CAS with eigenvals() I get √2+2, 2, 2-√2, ok ...
.............
Salvo

Last week I did an academic year project to one student just on this subject. All counted in detail, I used HP-50G only for the check of final result. DET, EGV, EGVL, REF, rref etc work well there (some results were necessary to finish manually them for the teacher). On HP-50 (Home+CAS+RPN in one mode) it was made much more conveniently than on Prime-emulator. I admire your enthusiasm.
It would be interesting to know in more details, what problem you work hard so?