RBM for parametric eigenvalue problems

[pmli]

It would be interesting to add support for parametric eigenvalue problems $A(\mu) x(\mu) = \lambda(\mu) x(\mu)$, where the goal is to approximate a few eigenvalues $\lambda(\mu)$ and/or the corresponding eigenvectors $x(\mu)$. For simplicity, $A(\mu)$ could be assumed to be Hermitian.

Here is some literature:

• L. Machiels, Y. Maday, I. B. Oliveira, A. T. Patera, and D. V. Rovas, 2000, Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, paper
• G. S. H. Pau, 2007, Reduced-basis method for band structure calculations, paper
• A. G. Buchan, C. C. Pain, F. Fang, and I. M. Navon, 2013, A POD reduced-order model for eigenvalue problems with application to reactor physics, paper
• T. Horger, B. Wohlmuth, and T. Dickopf, 2017, Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems, paper, preprint
• D. Frame, R. He, I. Ipsen, D. Lee, D. Lee, and E. Rrapaj, 2018, Eigenvector continuation with subspace learning, paper, preprint