Related papers: Convergent non complete interpolatory quadrature r…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
In this paper, we propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element…
We apply knot Floer homology to exhibit an infinite family of transversely nonsimple prime knots starting with $10_{132}$. We also discuss the combinatorial relationship between grid diagrams, braids, and Legendrian and transverse knots in…
The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the…
Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by…
In this note, we present an eighth-order derivative-free family of iterative methods for nonlinear equations. The proposed family shows optimal eight-order of convergence in the sense of the Kung and Traub conjecture \cite{5} and is based…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Although we will consider various shapes (e.g. we find all the…
We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.
We consider infinite parametric families of high degree number fields composed of quadratic fields with pure cubic, pure quartic, pure sextic fields and with the so called simplest cubic, simplest quartic fields. We explicitly describe an…
Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
A novel mathematical framework is derived for the addition of nodes to univariate and interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde matrix describing the relation between the…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.
We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.
A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of…
This paper is devoted to the construction and analysis of a Moser-Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of…
In this article, families of non-linear subdivision schemes are presented that are based on univariate polynomials up to degree three. Theses families of schemes are constructed by using dynamic iterative re-weighed least squares method.…