eigenval / EIGENVALUES

[salvomic]

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

[Archanus]

(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 !!!

[parisse]

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.

[salvomic]

(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!

[Hlib]

(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?

[salvomic]

(06-04-2015 08:37 PM)Hlib Wrote:  ...I admire your enthusiasm.
It would be interesting to know in more details, what problem you work hard so?

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

[Hlib]

(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!