On the midpoint quadrature formula for mappings with bounded variations and applications
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the positivity of certain Cotes numbers.
On the randomized complexity of Banach space valued integration
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by if and only if X is of equal norm type p.
On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals.
On weighted Ostrowski type inequalities for operators and vector-valued functions.
Optimal Addition of Knots to Cubature Formulae for Planar Regions.
Optimal combined quadrature formulas in Schmeisser's sense.
Optimal Convergence of Minimum Norm Approximations in Hp.
Optimal cubature formulas in a reflexive Banach space
Sequences of cubature formulas with a joint countable set of nodes are studied. Each cubature formula under consideration has only a finite number of nonzero weights. We call a sequence of such kind a multicubature formula. For a given reflexive Banach space it is shown that there is a unique optimal multicubature formula and the sequence of the norm of optimal error functionals is monotonically decreasing to 0 as the number of the formula nodes tends to infinity.
Optimal Quadrature Algorithms in Hp Spaces.
Optimal quadrature formulas in integral varieties.
Optimal quadrature formulas in the sense of Nikolski.
Optimal Quadrature of Hp Functions.
Optimal quadratures for a certain class of analytic functions
Orthogonal polynomials and quadrature.
Orthogonal polynomials on the semicircle