In this talk we present several representation theorems and averaging theorems for members of the difference class of secant updates introduced by Broadlie, Gourlay , and Greenstadt in 1973. The BFGS update is a well-known member of this difference class. We begin with the notion of an update kernel and use it to construct a new parametrization of the difference class of secant updates. Next we...

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...

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In this paper, we study how simple linear projections of some projective varieties behave when the projection center runs through the ambient space. More precisely, let X ⊂ P be a projective variety satisfying Green-Lazarsfeld’s property Np for some p ≥ 2, q ∈ P a closed point outside of X , and Xq := πq(X) ⊂ P the projected image of X from q. First, it is shown that the secant locus Σq(X) of X...

Let C ⊂ P be a smooth irreducible complete algebraic curve of degree d embedded in a projective 3-space over an algebraically closed field k. It is called n-regular if H(IC(n− 1)) = H(IC(n− 2)) = 0, where IC is the ideal sheaf of C. Among all this implies that the homogeneous ideal IC = ⊕ l H (IC(l)) ⊂ k[x0, x1, x2, x3] is generated in degree ≤ n ([7], Lecture 14) and C ⊂ P is (scheme-theoretic...

The secant method is the most used iterative to solve an operator equation where involved nondifferentiable. A known problem that arises when applying this its accessibility. Then, we try improve it by using technique of decomposition involved, so in turn sum two operators, one differentiable and other continuous but not differentiable. For this, use a family Newton-secant-type methods from New...