Concerning approximation with nodes

Recent Developments concerning Entropy and Approximation Numbers

Issues Concerning the Approximation Underlying the Spectral Representation Theorem

In many important textbooks the formal statement of the Spectral Representation Theorem is followed by a process version, usually informal, stating that any stationary stochastic process f (t), t 2 T g is the limit in quadratic mean of a sequence of processes fS(n, t), t 2 T g, each consisting of a finite sum of harmonic oscillations with stochastic weights. The natural issues, whether the appr...

Dataset concerning the analytical approximation of the Ae3 temperature

In this paper we present a new polynomial function for calculating the local phase transformation temperature (Ae3 ) between the austenite+ferrite and the fully austenitic phase fields during heating and cooling of steel:[Formula: see text] The dataset includes the terms of the function and the values for the polynomial coefficients for major alloying elements in steel. A short description of t...

On a Simultaneous Approximation Problem concerning Binary Recurrences

Let Rn (n = 0, 1, 2, . . .) be a second order linear recursive sequence of rational integers defined by Rn = ARn−1+BRn−2 for n > 1, where A and B are integers and the initial terms are R0 = 0, R1 = 1. It is known, that if α, β are the roots of the equation x2 −Ax−B = 0 and |α| > |β|, then Rn+1/Rn −→ α as n −→ ∞. Approximating α with the rational number Rn+1/Rn, it was shown that ∣∣∣α− Rn+1 Rn ∣...

Weighted quadrature rules with binomial nodes

In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...