We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: on-line learning with a simple square loss, and finding a symmetric positi...

In this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. To approach this aim the analytical formulas of secant stiffness matrix are presented. The models were validated and used to perform inve...

in this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.in the first approach, the equilibrium point of the system is one of the centers of the related membership fu...

The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...