Speaker
Description
I will present two projection methods for solving high-dimensional tensor eigenvalue problems with low-rank structure: an inexact Lanczos method and an inexact polynomial-filtered subspace iteration. The inexactness arises from low-rank compression, which enables efficient representation of high-dimensional vectors in low-rank tensor formats. A central challenge is that standard operations, such as matrix–vector products, increase tensor rank, necessitating rank truncation and thereby introducing approximation errors. Our numerical results show that subspace iteration is significantly more robust to truncation errors than the Lanczos method. Comparisons with the density matrix renormalization group (DMRG) method further demonstrate that subspace iteration can converge in regimes where DMRG stagnates. Overall, these results highlight inexact subspace iteration as a robust and effective approach for computing multiple eigenpairs of rank-structured tensor operators. A convergence analysis of inexact subspace iteration will also be presented.