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eigenval / EIGENVALUES - salvomic - 06-02-2015 09:50 PM
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 RE: eigenval / EIGENVALUES - Archanus - 06-03-2015 01:49 AM
(06-02-2015 09:50 PM)salvomic Wrote: I'm calculating eigenvalues of a matrix, [[2,-1,0],[-1,2,-1],[0,-1,2]]. I get the same error !!! RE: eigenval / EIGENVALUES - parisse - 06-03-2015 06:24 PM
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. RE: eigenval / EIGENVALUES - salvomic - 06-03-2015 06:58 PM
(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! RE: eigenval / EIGENVALUES - Hlib - 06-04-2015 08:37 PM
(06-02-2015 09:50 PM)salvomic Wrote: I'm calculating eigenvalues of a matrix, [[2,-1,0],[-1,2,-1],[0,-1,2]]. 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? RE: eigenval / EIGENVALUES - salvomic - 06-04-2015 09:06 PM
(06-04-2015 08:37 PM)Hlib Wrote: ...I admire your enthusiasm.thank you for admiration In this case no particular problem (I like much linear algebra); I've also HP 50g (wonderful), but I aim to understand the potentiality and the limits of the Prime with linear algebra. In the mean time I'm trying to implement something that Prime (for now) doesn't offer in simple way: LDU (and list of pivots), LDLt factorization and few (very few!) other things the Prime already don't have RE: eigenval / EIGENVALUES - Hlib - 06-04-2015 10:08 PM
(06-04-2015 09:06 PM)salvomic Wrote: ... In the mean time I'm trying to implement something that Prime (for now) doesn't offer in simple way: LDU (and list of pivots), LDLt factorization and few (very few!) other things the Prime already don't have I understand and do appreciate! |