The Grassmannian/Krĕın-space approach to interpolation theory introduced in the 1980s gives a Krĕın-space geometry approach to arriving at the resolvent matrix which parametrizes the set of solutions to a NevanlinnaPick interpolation or Nehari-Takagi best-approximation problem. We review the basics of this approach and then discuss recent extensions to multivariable settings which were not anti...

We present a new method of Speaker Adapted Training (SAT) that is more robust, faster, and results in lower error rate than the previous methods. The method, called Inverse Transform SAT (ITSAT) is based on removing the differences between speakers before training, rather than modeling the differences during training. We develop several methods to avoid the problems associated with inverting th...

We present a construction of a visually smooth surface which interpolates to position values and normal vectors of randomly distributed points on a 3D object. The method is local and uses quartic triangular and bicubic quadrilateral patches without splits. It heavily relies on an edge deleting algorithm which, starting from a given triangulation, derives a suitable combination of threeand four ...

Abstract In this paper, we extendthe structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, give explicit construction formulae the bases satisfy different types of interpolation conditions. First, establish analysis transfer function single-input single-output Then, extend these results case m...