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...

Exact moment equations for nonlinear Itô processes are derived. Taylor expansion of the drift and diffusion coefficients around the first conditional moment gives a hierarchy of coupled moment equations which can be closed by truncation or a Gaussian assumption. The state transition density is expanded into a Hermite orthogonal series with leading Gaussian term and the Fourier coefficients are ...

This paper describes an iterative method for factoring a polynomial that bears the same relation to Bairstow's method as the secant method in a single variable bears to Newton's method. Like the secant method, the generalized secant method requires only one function evaluation for each iteration, and like the secant method it converges to a simple factor with order (1+75)/2.

In this paper we analyze the use of structured quasi-Newton formulae as preconditioners of iterative linear methods when the inexact-Newton approach is employed for solving nonlinear systems of equations. We prove that superlinear convergence and bounded work per iteration is obtained if the preconditioners satisfy a Dennis-Moré condition. We develop a theory of LeastChange Secant Update precon...

In this work we study a class of Secant-like iterations for solving nonlinear and non-differentiable equations in Banach spaces. We consider a condition for divided differences which generalizes those usual ones, i.e, Lipschitz continuous and Hölder continuous conditions. A semilocal convergence result is obtained. For that, we use a technique based on a new system of recurrence relations to ob...

Historical Development of the BFGS Secant Method and Its Characterization Properties by Joanna Maria Papakonstantinou The BFGS secant method is the preferred secant method for finite-dimensional unconstrained optimization. The first part of this research consists of recounting the historical development of secant methods in general and the BFGS secant method in particular. Many people believe t...