A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton–Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are deriv...

In this paper, we use parametric form of fuzzy number, then feed-forward neural network is presented for obtaining approximate solution for fuzzy Fredholm integro-differential equation of the second kind. This paper presents a method based on neural networks and Newton-Cotes methods with positive coefficient. The ability of neural networks in function approximation is our main objective. The pr...

We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑

Our paper reviews Kallay’s results on a geometric version of the classic Newton-Raphson method, in the context of plane curve queries, e.g. curve-curve intersection, point-curve distance computation. Variants of the geometric Newton-Raphson methods are proposed and empirically verified.

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with n+ 1 nodes is used the resulting iterative method has convergence order at least n+ 2, starting with the case n = 0 (which corresponds to the Newton’s method).

The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class W r pðIÞ; Nikolskii class H pðIÞ and their periodic analogue is obtained. It is proved that if p41; then the stochastic and average error bounds are essentially smaller than the deterministic error bounds. Nonlinear methods, adaptive methods, or even method...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 4 January 2021Accepted: 07 June 2021Published online: 03 February 2022KeywordsGauss quadrature, Gauss--Hermite, Newton--Cotes, Clenshaw--Curtis, cubatureAMS Subject Headings41A55, 65D32Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for I...