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gams:calculating_eigenvalues

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 gams:calculating_eigenvalues [2007/09/27 04:51]127.0.0.1 external edit gams:calculating_eigenvalues [2007/10/21 06:27]Franz Nelissen 2020/05/28 07:57 Michael Bussieck 2007/10/21 06:27 Franz Nelissen 2007/10/21 06:27 Franz Nelissen 2007/09/27 04:51 external edit 2020/05/28 07:57 Michael Bussieck 2007/10/21 06:27 Franz Nelissen 2007/10/21 06:27 Franz Nelissen 2007/09/27 04:51 external edit Next revision Both sides next revision Line 63: Line 63: ​ - Another approach submitted by Arne Drud: ... Essentially,​ the eigenvalues are found one at a time from the largest + Another approach submitted by Arne Drud: Essentially,​ the eigenvalues are found one at a time from the largest - one using maximization. Each time an eigenvector has been found we require that the next eigenvectors are orthogonal. A little trick in the generation of initial values removes components parallel to already found eigenvectors and ensures that the initial point to each solve is feasible. All constraints except one are linear and the objective is + one using maximization. Each time an eigenvector has been found we require that the next eigenvectors are + orthogonal. A little trick in the generation of initial values removes components parallel ​ + to already found eigenvectors and ensures that the initial point to each solve is feasible. ​ + All constraints except one are linear and the objective is quadratic, so the model is easy to solve. quadratic, so the model is easy to solve. - - When I wrote the routine some years ago it was a little slow with many solves, but combined with the new solvelink option in GAMS it can actually solve medium sized instances quickly.... ​ <​code>​ <​code>​ \$Title First Covariance Matrix and its Eigen-values and -vectors. \$Title First Covariance Matrix and its Eigen-values and -vectors. + * Contributed ba Arne Drud (adrud@arki.dk) SETS SETS ​j ​         variables ​                           /j1*j25/ ​j ​         variables ​                           /j1*j25/