## UC Berkeley / Lawrence Berkeley Laboratory

#### Interpolation of Manifold-Valued Functions via the Polar Decomposition

**Evan Gawlik, University of California, San Diego**

##### November 1st, 2017 at 4:00PM–5:00PM in 891 Evans Hall [Map]

Manifold-valued data and manifold-valued functions play an important
role in a wide variety of applications, including mechanics, computer
vision and graphics, medical imaging, and numerical relativity. This
talk will describe a family of 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 acceleration-minimizing curves on the special
orthogonal group.