Errata-Corrigé : «Les coefficients optimaux des formules d'intégration approximative»
Erratum. Barycentric Formulae for Cardinal (SINC-) Interpolants.
Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)
Error autocorrection in rational approximation and interval estimates. [A survey of results.]
The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form of the effect which appears in rational approximations to functions. The error autocorrection effect occurs...
Error bounds for eigenvalues and eigenfunctions of some ordinary differential operators by the method of least squares
Error bounds for Gauss-Kronrod quadrature formulae of analytic functions.
Error Bounds for Rank 1 Lattice Quadrature Rules Modulo Composites.
Error Bounds for the Approximation of Green's Kernels by Splines.
Error bounds for two even degree tridiagonal splines.
Error estimate for quadratic spline interpolating the first derivatives
Error estimates and the Voronovskaja theorem for modified Szász-Mirakyan operators
Error estimates for approximating fixed points of quasi contractions.
Error estimates for approximation of translation invariant operators
Error Estimates for Gaussian Quadrature Formulae.
Error Estimates for Interpolatory Quadrature Formulae.
Error estimates for modified local Shepard’s formulas in Sobolev spaces
Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard’s partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard’s formulas, and...
Error estimates for Modified Local Shepard's Formulas in Sobolev spaces
Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard's partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard's formulas, and...
Error Estimates for Spline Interpolants on Equidistant Grids.
Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
Error estimates in the fast multipole method for scattering problems. Part 1 : truncation of the Jacobi-Anger series
We perform a complete study of the truncation error of the Jacobi-Anger series. This series expands every plane wave in terms of spherical harmonics . We consider the truncated series where the summation is performed over the ’s satisfying . We prove that if is large enough, the truncated series gives rise to an error lower than as soon as satisfies where is the Lambert function and are pure positive constants. Numerical experiments show that this asymptotic is optimal. Those results...