The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Finding equations in the ideal of secant varieties of Chow varieties would enable one to measure the complexity the permanent polynomial. In this article, I use the method of prolongation to obtain equations for secant varieties of Chow varieties as GL(V )-modules.

Another new family of Secant-like method is proposed in this paper. Analysis of convergence shows that the method has a super-linear convergence as Secant method. Numerical experiments show that the efficiency of the method is depended on the value of its parameter. AMS Subject Classification: 65D99, 65H05

We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing prolongations which are combinatorial in nature. As an application, we use prolongations to derive a new family of secant equations for the binary symmetric model i...

We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing prolongations which are combinatorial in nature. As an application, we use prolongations to derive a new family of secant equations for the binary symmetric model i...

In this work some interesting relations between results on basic optimization and algorithms for nonconvex functions (such as BFGS and secant methods) are pointed out. In particular, some innovative tools for improving our recent secant BFGS-type and LQN algorithms are described in detail. © 2006 Elsevier B.V. All rights reserved. MSC: 51M04; 65H20; 65F30; 90C53