From low-rank retractions to dynamical low-rank approximation and back
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A numerical algorithm that achieves asymptotic stability for feedback linearizable systems is presented. The nonlinear systems can be represented in various forms that include differential equations, simulated physical models or lookup tables. The proposed ...
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Isogeometric analysis (IGA) is a computational methodology recently developed to numerically approximate Partial Differential Equation (PDEs). It is based on the isogeometric paradigm, for which the same basis functions used to represent the geometry are t ...
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Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...
When dealing with multi-angular image sequences, problems of reflectance changes due either to illumination and acquisition geometry, or to interactions with the atmosphere, naturally arise. These phenomena interplay with the scene and lead to a modificati ...
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that are ob ...
Institute of Electrical and Electronics Engineers2013
We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kahler manifold M which preserves a submanifold N aS, M, the quotient M' = N/A has a natural Kahler structure. We verify that the assumptions on the grou ...
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In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT,k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group ac ...
