In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances invol...

Abstract With the motivation of avoiding the computation of the inverse of Jacobian matrix, which is involved in Newton’s method, we consider the use of vector divisions in solving a nonlinear system of equations F (x) = 0. Vector divisions are applied to form the secant method formulas. Based on that, a globally convergent hybrid algorithm for solving the nonlinear system of equations is propo...

At the beginning of this century, which is characterized by huge flows emerging data, Dai and Liao proposed a pervasive conjugacy condition that triggered interest many optimization scholars. Recognized as sophisticated conjugate gradient (CG) algorithm after about two decades, here we share our visions thoughts on method in framework review study. In regard, first discuss modified Dai–Liao met...

In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cros...

I find new equations for Chow varieties, their secant varieties, and an additional variety that arises in the study of complexity theory by flattenings and Koszul Young flattenings. This enables a new lower bound for symmetric border rank of x1x2⋯xd when d is odd, and a new lower complexity bound for the permanent.

Let X ⊂ P be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties.

Starting from the exact solution of heterogeneous linear viscoelastic Eshelby ellipsoidal inclusion problem obtained in time domain for an embedded isotropic matrix (Berbenni et al., 2015), a direct time-incremental homogenization Mori–Tanaka scheme two-phase non elasto-viscoplastic materials is proposed. The extension to non-linear behavior based on “modified secant” formulation obtain compari...

We introduce a three-step Chebyshev–Secant-type method (CSTM) with high efficiency index for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for (CSTM)using recurrence relations. Numerical examples validating our theoretical results are also provided in this study. © 2011 Elsevier B.V. All rights reserved.