Analytic Hessian matrices and the computation of FIGARCH estimates

Computation of the q-th roots of circulant matrices

In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.

Application of the Norm Estimates for Univalence of Analytic Functions

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.

Eigenvalue Estimates And Singularities Of Hessian Fields

Hessian Matrices via Automatic Differentiation

We investigate the computation of Hessian matrices via Automatic Differentiation, using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved in calculating the Hessian. The algebraic model, based on Griewank and Walther’s state transformations [7], synthesizes the calculation of the Hessian as a formula. These dual points of view, graphical and algebrai...

Exploiting Symmetry for Hessian Computation

Hessian computation in automatic differentiation can be implemented by applying elimination operations on a symmetric computational graph. We can exploit the symmetry by identifying pairs of symmetric operations and performing only one operation from each pair. Symmetry exploitation can potentially halve the number of operations. In this presentation, we describe an elimination algorithm that e...