Many problems in transportation can be formulated as fixed point problems, or equivalently as a systems of nonlinear equations, as for example multi-user equilibrium problems, planning problems, and consistent anticipatory route guidance generation. These fixed point problems are often characterized by the fact that there is no analytical form of the objective function, the computational cost o...

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our a...

Many applications in science and engineering lead to models which require solving large-scale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasi-Newton methods that implicitly update the approximate Jacobian or inverse Jacobian to satisfy a certain secant condition. We present two classes of multisec...

This report describes a new family of Newton-Krylov methods for solving nonlinear systems of equations arising from the solution of Richards’ equation and in fully implicit formulations in air-water systems. The basic approach is to perform secant (Broyden) updates restricted to the Krylov subspace generated by the GMRES iterative solver. This approach is introduced as Krylov-secant methods. On...

For Quasi-Newton methods, one of the most important challenges is to find an estimate Jacobian matrix as close possible real matrix. While in root-finding problems multi-secant methods are regularly used, optimization, it symmetric (in particular BFGS) that popular. Combining and single update formula would combine their benefits. However, can be proved symmetry property generally not compatibl...

Secant varieties to Veronese embeddings of projective space are classical varieties whose equations are not completely understood. Minors of catalecticant matrices furnish some of their equations, and in some situations even generate their ideals. Geramita conjectured that this is the case for the secant line variety of the Veronese variety, namely that its ideal is generated by the 3×3 minors ...

where F is a Fréchet-differentiable operator defined on an open subset D of a Banach space X with values in a Banach space Y . Finding roots of Eq.(1) is a classical problem arising in many areas of applied mathematics and engineering. In this study we are concerned with the problem of approximating a locally unique solution α of Eq.(1). Some of the well known methods for this purpose are the f...

We study the potential for controlled transfer of population to biexciton state a semiconductor quantum dot coupled with metal nanoparticle, under influence an electromagnetic pulse hyperbolic secant shape, and derive analytical solutions density matrix equations, both zero nonzero energy shift. These lead efficient state, various interparticle distances, including relatively small values. In c...