Abstract This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space ( ) 2 (0,1) m L . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number 1 N m ≥ ...

This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature...

We compute quadrature weights for scattered nodes on the two-dimensional unit-sphere, which are exact for spherical polynomials of high degree N . Different algorithms are proposed and numerical examples show that we can compute nonnegative quadrature weights if approximately 4N2/3 well distributed nodes are used. We compare these results with theoretical statements which guarantee nonnegative ...

This is a selection of facts, old and new, about quadrature domains. The text, written in the form of a survey, is addressed to non-experts and covers a variety of phenomena related to quadrature domains. Such as: the difference between quadrature domains for subharmonic, harmonic and respectively complex analytic functions, geometric properties of the boundary, instability in the reverse Hele-...

Despite the advantages that quadrature mixing offers to radio front-ends, its practical use has been limited due to its sensitivity towards gain and phase mismatches between its in-phase and quadrature channels. DC offsets are also a problem when a zero-IF transceiver topology is used. In this paper, novel digital compensation techniques are introduced to extract and correct the quadrature imba...

We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O’Hara and Smith in the 1960s, the phenomenon is explained as ...

In this paper we suggest a Stata routine for multinomial logit models with unobserved heterogeneity using maximum simulated likelihood based on Halton sequences. The purpose of this paper is twofold: First, we provide a description of the technical implementation of the estimation routine and discuss its properties. Further, we compare our estimation routine to the Stata program gllamm which so...

The paper reviews the relation between Padé-type approximants of a power series and interpolatory quadrature formulas with free nodes, and that between Padé approximants and Gaussian quadrature methods. Quadrature methods are well-known. They are used for obtaining an approximate value of a definite integral, and are described in any book of numerical analysis. In this talk, we will show that P...

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...

Quadrature rules estimate ∫ 1 0 f(x) dx when f is defined by a table of n+1 values. Every binary string of length n defines a quadrature rule by choosing which endpoint of each interval represents the interval. The standard rules, such as Simpson’s Rule, correspond to strings of low Kolmogorov complexity, making it possible to define new quadrature rules with no smoothness assumptions, as well ...