T -adic exponential sums associated to a Laurent polynomial f are introduced. They interpolate all classical p-power order exponential sums associated to f . The Hodge bound for the Newton polygon of L-functions of T -adic exponential sums is established. This bound enables us to determine, for all m, the Newton polygons of Lfunctions of p-power order exponential sums associated to an f which i...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present a...

Superlinear convergence of the Newton method for nonsmooth equations requires a “semismoothness” assumption. In this work we prove that locally Lipschitz functions definable in an o-minimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth. Semialgebraic, or more generally, globally subanalytic mappings present the special interest of being γ -order semism...

in this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

This paper is a continuation of our previous paper [3] were we presented generalizations of the Dennis-Moré theorem to characterize q-superliner convergences of quasi-Newton methods for solving equations and variational inequalities in Banach spaces. Here we prove Dennis-Moré type theorems for inexact quasi-Newton methods applied to variational inequalities in finite dimensions. We first consid...

Large-scale simulations in spherical geometries require associated quadrature formulas. Classical approaches based on tabulated weights are limited to specific quasi-uniform distributions of relatively low numbers of nodes. By using a radial basis function-generated finite differences (RBF-FD) based approach, the proposed algorithm creates quadrature weights for N arbitrarily scattered nodes in...

Tensor-product approximation provides a convenient tool for efficient numerical treatment of high dimensional problems that arise, in particular, in electronic structure calculations in Rd. In this work we apply tensor approximation to the Galerkin representation of the Newton and Yukawa potentials for a set of tensor-product, piecewise polynomial basis functions. To construct tensor-structured...

The reconstruction of spectral function from correlation in Euclidean space is a challenging task. In this paper, we employ the Machine Learning techniques terms radial basis functions networks to reconstruct finite number data. To test our method, first generate one type data using mock by mixing several Breit-Wigner propagators. We found that compared with other traditional methods, TSVD, Tik...

Superlinear convergence of the Newton method for nonsmooth equations requires a “semismoothness” assumption. In this work we prove that locally Lipschitz functions definable in an o-minimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth. Semialgebraic, or more generally, globally subanalytic mappings present the special interest of being γ-order semismo...