Gaussian Integration in the Presence of a Singularity

In this paper, we study the singularity of multivariate Hermite interpolation of type total degree. We present two methods to judge the singularity of the interpolation schemes considered and by methods to be developed, we show that all Hermite ...

We consider parametric curves that are represented by combination of control points and basis functions. We let a control point vary while the rest is held fixed. We show that the locus of the moving control point that yields a zero curvature point on ...

Singularities in the parameter spaces of hierarchical learning machines are known to be a main cause of slow convergence of gradient descent learning. The EM algorithm, which is another learning algorithm giving a maximum likelihood estimator, is also ...