Abstract by Suzanna Stephenson
Dimensionality Reduction in Multivariate Rootfinding
We have developed multivariate root-finding methods that rely on polynomial approximations to the original functions. This has many advantages, one of which is the potential to reduce the dimensionality of the problem when one of the polynomial approximations is linear. In this talk, I will discuss the benefits and drawbacks of several methods to perform this dimensionality reduction. These methods include (1) re-approximating the nonlinear functions on the hyperplane defined by the approximately-linear function, (2) performing explicit variable substitutions in Chebyshev form, and (3) removing a variable in the spectral problem used to identify roots.