in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

A local and semi-local convergence is developed of a class iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions first-order divided differences. Special cases this method are well-known algorithms, in particular, Secant, Kurchatov, Steffensen as well Newton method. For analysis, we use technique recurrent fun...

This paper presents a novel procedure for solving the equations system of the rotating crack model used for reinforced concrete. It is implemented in the programme NonOPt where it is used to optimise the reinforcement design of D regions. The procedure is based on solving explicit closed-form relations without the need to incrementally increase the applied loads. The solution procedure is based...

Tropical geometry yields good lower bounds, in terms of certain combinatorialpolyhedral optimisation problems, on the dimensions of secant varieties. In particular, it gives an attractive pictorial proof of the theorem of Hirschowitz that all Veronese embeddings of the projective plane except for the quadratic one and the quartic one are non-defective; this proof might be generalisable to cover...

Let O be a conic in the classical projective plane PG(2, q), where q is an odd prime power. With respect to O, the lines of PG(2, q) are classified as passant, tangent, and secant lines, and the points of PG(2, q) are classified as internal, absolute and external points. The incidence matrices between the secant/passant lines and the external/internal points were used in [5] to produce several ...

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 paper, we design a new model of preconditioner for systems of linear equations. the convergence properties of the proposed methods have been analyzed and compared with the classical methods. numerical experiments of convection-diffusion equations show a good im- provement on the convergence, and show that the convergence rates of proposed methods are superior to the other modified itera...