The semilocal convergence of the secant method under Hölder continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the follo...

We compare the Ostrowski efficiency of some methods for solving systems of nonlinear equations without explicitly using derivatives. The methods considered include the discrete Newton method, Shamanskii’s method, the two-point secant method, and Brown’s methods. We introduce a class of secant methods and a class of methods related to Brown’s methods, but using orthogonal rather than stabilized ...

The goal of this talk is to introduce secant varieies and show connections of secant varieties of Veronese variety to the Waring problem. 1 Secant varieties Let X ⊂ P be a variety over k, where k is algebraically closed field of characteristic 0 (or just assume k = C). Definition 1.1. For s ≥ 1 the s-th higher secant variety of X is

we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

This paper presents an improved diagonal Secant-like method using two-step approach for solving large scale systems of nonlinear equations. In this scheme, instead of using direct updating matrix in every iteration to construct the interpolation curves, we chose to use an implicit updating approach to obtain an enhanced approximation of the Jacobian matrix which only requires a vector storage. ...

The border rank of the matrix multiplication operator for n× n matrices is a standard measure of its complexity. Using techniques from algebraic geometry and representation theory, we show the border rank is at least 2n2−n. Our bounds are better than the previous lower bound (due to Lickteig in 1985) of 2 n 2 + 2 −1 for all n≥ 3. The bounds are obtained by finding new equations that bilinear ma...

We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality statements about SecX and also to obtain information about linear systems on the blow up of projective space along a variety X. We use these results to geometrica...