Hi,
I just stumbled upon a cool algorithm that I'd like to try out. It requires that I solve a Quadratic Eigen Value problem. The article mentions that I can do this in Matlab using the 'polyeig' function. Unfortunately it seems that Octave doesn't have this function :-( Does anybody know how to solve such problems with Octave? Søren _______________________________________________ Help-octave mailing list [hidden email] https://www.cae.wisc.edu/mailman/listinfo/help-octave |
Hi, S!)ren
consider the following problem: lambda^2 A u + lambda B u + C u == 0, where 0 is zero vector; lambda is unknown scalar; u is unknwon vector; A,B and C are given matrices. introduce auxiliary vector v as follows. v= lambda u. the problem is transformed to: lambda A v + lambda B u == -C u, lambda u == v. matrix representation of this problem is lambda [[B A];[I 0]] * [u;v] == [-C; I][u:v], where I is unit matrix. this is a generalized eigenvalue problem. octave function qz can be applied to this problem. Reference: SIAM Review Vol. 43 No. 2 pp. 235--286, F. Tisseur and K. Meerbergen, "The quadratic eigenvalue problem" 2007-07-12, 15:52 JST, "S!)ren Hauberg" <[hidden email]> wrote: >Hi, > I just stumbled upon a cool algorithm that I'd like to try out. It >requires that I solve a Quadratic Eigen Value problem. The article >mentions that I can do this in Matlab using the 'polyeig' function. >Unfortunately it seems that Octave doesn't have this function :-( > Does anybody know how to solve such problems with Octave? > >S!)ren _______________________________________________ Help-octave mailing list [hidden email] https://www.cae.wisc.edu/mailman/listinfo/help-octave |
Hi,
Thanks a lot for the answer! I should be able to implement the algorithm now. Thanks, Søren Fumihiro CHIBA skrev: > Hi, S!)ren > > consider the following problem: > lambda^2 A u + lambda B u + C u == 0, > where 0 is zero vector; lambda is unknown scalar; > u is unknwon vector; A,B and C are given matrices. > > introduce auxiliary vector v as follows. > v= lambda u. > the problem is transformed to: > lambda A v + lambda B u == -C u, > lambda u == v. > > matrix representation of this problem is > lambda [[B A];[I 0]] * [u;v] == [-C; I][u:v], > where I is unit matrix. > this is a generalized eigenvalue problem. > octave function qz can be applied to this problem. > > Reference: > SIAM Review Vol. 43 No. 2 pp. 235--286, > F. Tisseur and K. Meerbergen, "The quadratic eigenvalue problem" > > 2007-07-12, 15:52 JST, "S!)ren Hauberg" <[hidden email]> wrote: >> Hi, >> I just stumbled upon a cool algorithm that I'd like to try out. It >> requires that I solve a Quadratic Eigen Value problem. The article >> mentions that I can do this in Matlab using the 'polyeig' function. >> Unfortunately it seems that Octave doesn't have this function :-( >> Does anybody know how to solve such problems with Octave? >> >> S!)ren > Help-octave mailing list [hidden email] https://www.cae.wisc.edu/mailman/listinfo/help-octave |
In reply to this post by Fumihiro CHIBA
Sorry, I mistook.
#Correction: On Thursday, July 12, 2007, at 05:18PM, "Fumihiro CHIBA" <[hidden email]> wrote: >lambda [[B A];[I 0]] * [u;v] == [-C; I][u:v], >where I is unit matrix. lambda [[B A]; [I 0]] * [u; v] == [-C 0; 0 I]*[u; v], where I is unit matrix. _______________________________________________ Help-octave mailing list [hidden email] https://www.cae.wisc.edu/mailman/listinfo/help-octave |
In reply to this post by Søren Hauberg
Søren Hauberg wrote:
> Hi, > Thanks a lot for the answer! I should be able to implement the > algorithm now. > > Thanks, > Søren > Hey this is the basis on the polyeig function itself. If you are going to implement something maybe writing polyeig itself might be a good idea :-) D. -- David Bateman [hidden email] Motorola Labs - Paris +33 1 69 35 48 04 (Ph) Parc Les Algorithmes, Commune de St Aubin +33 6 72 01 06 33 (Mob) 91193 Gif-Sur-Yvette FRANCE +33 1 69 35 77 01 (Fax) The information contained in this communication has been classified as: [x] General Business Information [ ] Motorola Internal Use Only [ ] Motorola Confidential Proprietary _______________________________________________ Help-octave mailing list [hidden email] https://www.cae.wisc.edu/mailman/listinfo/help-octave |
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