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oseledets / TT-Toolbox

The git repository for the TT-Toolbox
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How to solve generalized eigenvalue problems using TT-Toolbox? #67

Open 7alent opened 6 months ago

7alent commented 6 months ago

I'm trying to solve a generalized eigenvalue problem but I have no idea what functions in this toolbox I should use. Are there any eigenvalue solvers in this toolbox? I really appreciate it if you could give me some advice.

dolgov commented 6 months ago

We never had to solve nontrivial generalized eigenvalue problems, so there is no function for this. For the standard eigenvalue problems there is dmrg_eig, implementing Computation of extreme eigenvalues in higher dimensions using block tensor train format. If the Cholesky decomposition of the B matrix is easy, you can pre- and post-multiply A with the Cholesky factors to turn the generalized eigenvalue problem into the standard eigenvalue problem. Otherwise you'd need to update the code to project B in addition to A and solve local generalized eigenvalue problems.

7alent commented 6 months ago

Sincerely thank you for taking time out of your busy schedule and replying my question. As a first-year postgraduate majoring in Computational Mathematics, I'm learning FEM-QTT and this toolbox really helps me a lot.