RTRESGEV contains implementations of Riemannian Trust-Region methods for the computation of Extreme Generalized Symmetric Eigenvalues. This software provides two separate eigenvalue solvers: one based on the Riemannian trust-region (RTR) method and the other based on the implicit Riemannian trust-region (IRTR) method. Both are block, preconditioned eigensolvers with provably robust global convergence properties and superlinear local convergence.
RTRESGEV currently provides implementations in MATLAB, with implementations of the IRTR solvers in Trilinos/Anasazi in the Trilinos 9 release (Oct 2008). These are specially tailored implementations of the RTR methods for this problem; for more general implementations applicable to a wider variety of Riemannian optimization problems, see the GenRTR package.
The solvers implement the RTR and IRTR Riemannian optimization solvers applied to the problem of minimizing the generalized Rayleigh quotient over the Grassmann manifold. Given a matrix pencil (A,B), where A is symmetric/Hermitian and B is symmetric/Hermitian positive definite, the solvers compute the leftmost (i.e., smallest algebraic) eigenvalues of (A,B). To compute the rightmost eigenvalues, submit the pencil (-A,B).
RTR and IRTR solvers for general Riemannian optimization:
- Trust-region methods on Riemannian manifolds
- An implicit trust-region method on Riemannian manifolds
Eigenvalue-specific applications:
- A truncated-CG style method for symmetric generalized eigenvalue problems
- An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenvalue Problem
- Adaptive model trust region methods for generalized eigenvalue problems
- Chris Baker, NVIDIA
- Pierre-Antoine Absil, Université catholique de Louvain
- Kyle Gallivan, Florida State University
- National Science Foundation Award 032944: "Collaborative Research: Model Reduction of Dynamical Systems for Real Time Control"
- National Science Foundation Award 9912415: "Efficient Algorithms for Large Scale Dynamical Systems"
- JD Gateway
- Andrew Knyazev's preconditioned eigensolvers page
- GenRTR package — general Riemannian optimization