Equally-weighted quadrature formulas for inversion integrals

Quadrature Rules for Fuzzy Integrals

Compact Numerical Quadrature Formulas for Hypersingular Integrals and Integral Equations

In the first part of this work, we derive compact numerical quadrature formulas for finite-range integrals I [f ] = ∫ b a f (x) dx, where f (x)= g(x)|x − t |β , β being real. Depending on the value of β, these integrals are defined either in the regular sense or in the sense of Hadamard finite part. Assuming that g ∈ C∞[a, b], or g ∈ C∞(a, b) but can have arbitrary algebraic singularities at x ...

Quadrature formulas for integrals transforms generated by orthogonal polynomials

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...

Chebyshev series method for computing weighted quadrature formulas

In this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions. The main goal is to evaluate accurately a definite integral, whose mass is highly concentrated near some points. The numerical implementation of this approach is based on the calculation of Chebyshev series and some integration formulas which are exact for ...

Weighted Norm Estimates and Representation Formulas for Rough Singular Integrals

Weighted norm estimates and representation formulas are proved for nonhomogeneous singular integrals with no regularity condition on the kernel and only an L logL integrability condition. The representation formulas involve averages over a starshaped set naturally associated with the kernel. The proof of the norm estimates is based on the representation formulas, some new variations of the Hard...