Search results for " 15A69"
showing 3 items of 3 documents
Existence of dynamical low-rank approximations to parabolic problems
2021
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.
The Rank of Trifocal Grassmann Tensors
2019
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…
Jordan Decompositions of Tensors
2022
We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra which acts on it and embed them into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information.