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 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
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## Re: Quadratic Eigen value problems?

 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
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## Re: Quadratic Eigen value problems?

 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
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## Re: Quadratic Eigen value problems?

 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