Gaussian quadratures for a broad class of functions. While some of the components of this algorithm have been previously published, we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works. The performance of the resulting procedure is illustrated...

We show how to combine incidence matrices, which admit Hermite-Birkhoff quadrature formulas of Gaussian type for any positive measure, in such a way that the resulting matrix also admits Gaussian type quadratures for any positive measure. Moreover, the uniqueness property and the extremal property of the formulas corresponding to the submatrices are transferred to the formula admitted by the co...

In this paper we consider an application of a special class of little 1/q-Jacobi polynomials to summation of series. Beside the three-term recurrence relation for such polynomials, a zero distribution as well as the corresponding quadratures of Gaussian type are investigated. Some numerical examples are included.

The newly developed iterative method based on Green function defined by quadratures along a single trajectory is combined with the variational method to solve the ground state quantum wave function for central potentials. As an example , the method is applied to discuss the ground state solution of Yukawa potential, using Hulthen solution as the trial function.

An example of application of the specialized computer algebra system GRGEC to the searching for solutions to the source-free Maxwell and Einstein–Maxwell equations is demonstrated. The solution involving five arbitrary functions of two variables is presented in explicit form (up to quadratures).

In this paper we characterize rational Szegő quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szegő quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experime...

we de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

Two spatial, one axisymmetric and two plane contact problems are considered for a transversely isotropic elastic layer with face subjected to sliding support. In the spatial problems, planes of isotropy may be either parallel or perpendicular faces. case axial symmetry, By using Fourier integral transforms, reduced equations respect pressure, limiting cases which well-known corresponding an lay...

We study the dependence of functions capital (resource) and consumption in Ramsey–Kass–Koopmans economic model case when saving is an identical constant. The system differential equations describing evolution under consideration solved quadratures assumptions made. Upper estimates function are found based on obtained solution.

Central schemes offer a simple and versatile approach for computing approximate solutions of non-linear systems of hyperbolic conservation laws and related PDEs. The solution of such problems often involves the spontaneous evolution of steep gradients. The multiscale aspect of these gradients poses a main computational challenge for their numerical solution. Central schemes utilize a minimal am...