Quadrature and harmonic $L\sp 1$-approximation in annuli

Approximation and Quadrature

Let V be a vector space with inner product (u, v) and norm u = (u, u) 1/2. We are given u ∈ V and a subspace˜V = span v (n) are linearly independent. We want to find p ∈ ˜ V such that u − p is minimal.

Approximation Algorithms for Minimum-Width Annuli and Shells

fragmentability and approximation

in chapter 1, charactrizations of fragmentability, which are obtained by namioka (37), ribarska (45) and kenderov-moors (32), are given. also the connection between fragmentability and its variants and other topics in banach spaces such as analytic space, the radone-nikodym property, differentiability of convex functions, kadec renorming are discussed. in chapter 2, we use game characterization...

Hermite-Pade' approximation and simultaneous quadrature formulas

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and positivity of the corresponding quadrature coe...

Infinite-Dimensional Quadrature and Approximation of Distributions

We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown to be closely related to the problem of quantization and to the average Kolmogorov widths of the underlying probability measure. In addition to the general setting we analyze in particular integration w.r.t. Gaussian measur...