"Optimal quadrature formulas for approximate solution of the rst kind singular integral equation with Cauchy kernel"

Abstract

"In the present paper in $L_2^{(m)}(-1,1)$ space the optimal quadrature formulas with derivatives are constructed for approximate solution of a singular integral equation of the first kind with Cauchy kernel. Approximate solution of the singular integral equation is obtained applying the optimal quadrature formulas. Explicit forms of coefficients for the of optimal quadrature formulas are obtained. Some numerical results are presented."

Perfect Quadratic Forms Connected With a Lattice and Cubature Formulas

“…Many mathematicians have studied the construction of lattice optimal cubature and quadrature formulas [18][19][20][21][22][23][24][25][26][27][28].…”

Approximation of the Hilbert transform in the Lebesgue spaces

“…Many papers have dealt with the numerical approximation of the Hilbert Transform in the case of bounded intervals and the reader can refer to [1,3,6,7,9,10,12,13,15,16,17,20,21,22,25,28,30,31,32,37,38] and the references given there. On the other hand, the literature concerning the numerical integration on unbounded intervals is by far poorer than the one on bounded intervals.…”