We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian
connection, parallel translation, geodesics and distance on the Grassmann manifold of p …

We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from
adiabaticity, we find a Riemannian metric tensor underlying adiabatic evolution. Equipped …

Model order reduction helps to reduce the computational time in dealing with large
dynamical systems, for example, during simulation, control, optimization. In many cases, the …

Abstract Proper Orthogonal Decomposition (POD) basis interpolation on Grassmann
manifolds has been successfully applied to problems of parametric model order reduction …

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces
of \rr^n and converges locally cubically to the invariant subspaces of a symmetric matrix …

This article deals with the Grassmann manifold as a submanifold of the matrix Euclidean
space, that is, as the set of all orthogonal projection matrices of constant rank, and sets up …

Direct transcription methods are a popular approach for solving optimal control problems.
They are sometimes able to solve problems that the classical numerical theory would …

We adapt the notion of processes to introduce an abstract framework for dynamics in finite
time, ie on compact time-sets. For linear finite-time processes a notion of hyperbolicity …

We report a proof that under natural assumptions shock profiles viewed as heteroclinic
travelling wave solutions to a hyperbolically regularized system of conservation laws are …

Tangent and normal cones play an important role in constrained optimization to describe
admissible search directions and, in particular, to formulate optimality conditions. They …