eigenval / EIGENVALUES

06022015, 09:50 PM
Post: #1




eigenval / EIGENVALUES
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 ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

06032015, 01:49 AM
Post: #2




RE: eigenval / EIGENVALUES  
06032015, 06:24 PM
Post: #3




RE: eigenval / EIGENVALUES
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.


06032015, 06:58 PM
Post: #4




RE: eigenval / EIGENVALUES
(06032015 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! ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

06042015, 08:37 PM
Post: #5




RE: eigenval / EIGENVALUES
(06022015 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 HP50G 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 HP50 (Home+CAS+RPN in one mode) it was made much more conveniently than on Primeemulator. I admire your enthusiasm. It would be interesting to know in more details, what problem you work hard so? 

06042015, 09:06 PM
Post: #6




RE: eigenval / EIGENVALUES
(06042015 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 ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

06042015, 10:08 PM
Post: #7




RE: eigenval / EIGENVALUES  
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