Thread Subject:

linear generalized real symmetric eigenvalue problem

hi.
i am solving a physics problem, and i need to solve eigenvalue
eguation: A.X=Lamda.B.X. A and B are symmetric, and B is not positive
definite.
all of the elements of B are nonnegative.
the matrices are at most 100 by 100.
could anyone help me white this problem? i need to know fortran
subroutines that can solve this problem accurately.
in advance i appriciate your help.

> hi.
> i am solving a physics problem, and i need to solve
> eigenvalue
> eguation: A.X=Lamda.B.X. A and B are symmetric, and B
> is not positive
> definite.
> all of the elements of B are nonnegative.
> the matrices are at most 100 by 100.
> could anyone help me white this problem? i need to
> know fortran
> subroutines that can solve this problem accurately.
> in advance i appriciate your help.

Try
http://www.caam.rice.edu/software/ARPACK/

Best wishes
Torsten.

i am going to try that.
thank you very much.

rain <taherehnikbakht@gmail.com> wrote in message <0b7c7704-f8c4-492d-9e10-2e5bdb08accc@m22g2000vbp.googlegroups.com>...
> hi.
> i am solving a physics problem, and i need to solve eigenvalue
> eguation: A.X=Lamda.B.X. A and B are symmetric, and B is not positive
> definite.
> all of the elements of B are nonnegative.
> the matrices are at most 100 by 100.
> could anyone help me white this problem? i need to know fortran
> subroutines that can solve this problem accurately.
> in advance i appriciate your help.

  The matlab function 'eig' can handle that problem.

[V,D] = eig(A,B);

Roger Stafford

Hi Roger,

I am currently facing the same situation as Rain above. You are right about the 'eig' function, but with this function Matlab solves his own version of the generalized eigenvalue problem:
[X,Lambda] = eig(A,B) solves
A*X = B*X*Lambda,
but not the "real" GEP in which me and Rain were interested:
A*X = Lambda*B*X,
which are not the same, as they are all matrices.
I tried to work around this with some algebra, without success.
Strangely, using
[AA,BB,Q,Z,X_L,X_R] = qz(A,B),
gives the eigenvalue matrix
Lambda = diag(diag(AA)/(diag(BB)),
and the equalities
A*X_R = B*X_R*Lambda
transpose(X_L)*A = Lambda*transpose(X_L)*B.
Again, simple algebra doesn't let me transform this into the "real" GEP.
In my case, A and B are symmetric as well.

Am I overlooking some option or algebra trick?

Thanks in advance,

Thom

"Roger Stafford" wrote in message <gm1lmm$fbr$1@fred.mathworks.com>...
> rain <taherehnikbakht@gmail.com> wrote in message <0b7c7704-f8c4-492d-9e10-2e5bdb08accc@m22g2000vbp.googlegroups.com>...
> > hi.
> > i am solving a physics problem, and i need to solve eigenvalue
> > eguation: A.X=Lamda.B.X. A and B are symmetric, and B is not positive
> > definite.
> > all of the elements of B are nonnegative.
> > the matrices are at most 100 by 100.
> > could anyone help me white this problem? i need to know fortran
> > subroutines that can solve this problem accurately.
> > in advance i appriciate your help.
>
> The matlab function 'eig' can handle that problem.
>
> [V,D] = eig(A,B);
>
> Roger Stafford

"Thom de Jong" <bluecarme@hotmail.com> wrote in message
> but not the "real" GEP in which me and Rain were interested:
> A*X = Lambda*B*X,

Are you sure about the claim this it tghe real "GEP"?

It looks to me more like a non-sense equation, since if I multiply by inv(X) on the right, it leads to

A = Lambda*B

Which mean A-rows and B-rows are colinears, which is impossible in general.

Bruno

Interesting, it is a non-sense equation;
After going through the mathematics of the paper that made me come to this problem, there was indeed an index error. The equation to solve turns out to be the one implemented in Matlab.

Many thanks,

Thom


"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <jmmejd$n9l$1@newscl01ah.mathworks.com>...
> "Thom de Jong" <bluecarme@hotmail.com> wrote in message
> > but not the "real" GEP in which me and Rain were interested:
> > A*X = Lambda*B*X,
>
> Are you sure about the claim this it tghe real "GEP"?
>
> It looks to me more like a non-sense equation, since if I multiply by inv(X) on the right, it leads to
>
> A = Lambda*B
>
> Which mean A-rows and B-rows are colinears, which is impossible in general.
>
> Bruno