eigenval / EIGENVALUES
06-02-2015, 09:50 PM
Post: #1
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
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
06-03-2015, 01:49 AM
Post: #2
 Archanus Member Posts: 53 Joined: Dec 2014
RE: eigenval / EIGENVALUES
(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 !!!
06-03-2015, 06:24 PM
Post: #3
 parisse Senior Member Posts: 1,242 Joined: Dec 2013
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.
06-03-2015, 06:58 PM
Post: #4
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: eigenval / EIGENVALUES
(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!

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-04-2015, 08:37 PM
Post: #5
 Hlib Member Posts: 242 Joined: Jan 2015
RE: eigenval / EIGENVALUES
(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?
06-04-2015, 09:06 PM
Post: #6
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: eigenval / EIGENVALUES
It would be interesting to know in more details, what problem you work hard so?
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
06-04-2015, 10:08 PM
Post: #7
 Hlib Member Posts: 242 Joined: Jan 2015
RE: eigenval / EIGENVALUES
(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!
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)