Session A5 - Geometric Integration and Computational Mechanics
July 12, 16:00 ~ 16:30 - Room 111
Interpolation of Manifold-Valued Functions via the Generalized Polar Decomposition
University of California, San Diego, United States - firstname.lastname@example.org
We construct interpolation operators for manifold-valued functions, with an emphasis on functions taking values in symmetric spaces and Lie groups. A key role in our construction is played by the polar decomposition -- the well-known factorization of a real nonsingular matrix into the product of a symmetric positive-definite matrix times an orthogonal matrix -- and its generalization to Lie groups. We demonstrate that this factorization can be leveraged to carry out a number of seemingly disparate tasks, including the design of finite elements for numerical relativity, the interpolation of subspaces for reduced-order modeling, and the approximation of Riemannian cubics on the special orthogonal group.
Joint work with Melvin Leok (University of California, San Diego).