We introduce new families of Gaussian-type quadratures for weighted integrals of exponential functions and consider their applications to integration and interpolation of bandlimited functions. We use a generalization of a representation theorem due to Carathéodory to derive these quadratures. For each positive measure, the quadratures are parameterized by eigenvalues of the Toeplitz matrix con...

Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. Especially, curvature estimation of a mesh is an active research area [GI04, CSM03, CP03] with many applications. The most important curvature measures on a surface are the mean curvature H, the Gaussian curvature K, and the curv...

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi,...

We reformulate the Johnson–Nedelec approach for the exterior two-dimensional Stokes problem taking advantage of the parameterization of the artificial boundary. The main aim of this paper is the presentation and analysis of a fully discrete numerical method for this problem. This one responds to the needs of having efficient approximate quadratures for the weakly singular boundary integrals. We...

We investigate in this paper problems of theoretical foundation of collocations and mechanical quadratures methods for approximate solution of singular integral equation systems in the case, when their symbols have on the integration contour a finite set of integer degree zeroes. We consider the case when equation digitalization points are taken in such a way that each point of the contour can ...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

The finite temperature Lanczos method (FTLM), which is an exact diagonalization intensively used in quantum many-body calculations, formulated the framework of orthogonal polynomials and Gauss quadrature. main idea to reduce static dynamic quantities into weighted summations related one- two-dimensional quadratures. Then lower order quadrature, generated from iteration, can be applied approxima...

The paper considers a class of nonlinear differential equations which are not solvable in quadratures general case. author’s technology for solving such contains six problems. In this article, the solution to one these problems is given, real area it possible calculate an analytical approximate case value moving singular point obtained. Obtained results based on application elements calculus fi...

Abstract We present a family of high-order trapezoidal rule-based quadratures for class singular integrals, where the integrand has point singularity. The part is expanded in Taylor series involving terms increasing smoothness. are based on rule, with quadrature weights Cartesian nodes close to singularity judiciously corrected expansion. High-order accuracy can be achieved by utilizing suffici...