For a germ of a meromorphic function f = P Q , we offer notions of the mono-dromy operators at zero and at infinity. If the holomorphic functions P and Q are non-degenerated with respect to their Newton diagrams, we give an analogue of the formula of Varchenko for the zeta-functions of these monodromy operators. A polynomial f of (n + 1) complex variables of degree d determines a meromorphic fu...

in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Control theory has become a focus of research for evaluation and synthesis of numerical algorithms. In this paper, a finite-time version of the continuous Newton method is proposed using finite-time stability theory. Moreover, robustness of the proposed method under computational errors is discussed. It is also shown that the proposed approach can change the singularity structure of the Newton ...

We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...

In this paper we provide a new method to certify that nearby polynomial system has singular isolated root and compute its multiplicity structure. More precisely, given f=(f1,…,fN)∈C[x1,…,xn]N, present Newton iteration on an extended deflated locally converges, under regularity conditions, small deformation of f such deformed exact root. The simultaneously converges the coordinates coefficients ...

Introduction: Since preserving the structure of treated teeth is a critical success factor, studying the effects of tooth structure loss on fracture resistance of the tooth tissue appears necessary. The aim of this study was to evaluate the consequences of the loss of different tissues regarding fracture resistance of teeth undergoing root canal treatment without the use of indirect restoration...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...