The classical theory of Gaussian quadrature assumes a positive weight function. We will show that in some cases Gaussian rules can be constructed with respect to an oscillatory weight, yielding methods with complex quadrature nodes and positive weights. These rules are well suited for highly oscillatory integrals because they attain optimal asymptotic order. We show that for the Fourier oscilla...

Economists recognize that results from simulation models are dependent, sometimes highly dependent, on values employed for critical exogenous variables. To account for this, analysts sometimes conduct sensitivity analysis with respect to key exogenous variables. This paper presents a practical approach for conducting systematic sensitivity analysis, called Gaussian quadrature. The approach view...

The Jacobi matrix of the (2n+1)-point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the Jacobi-Kronrod matrix analytically. The nodes and weights can then be computed directly by standard software for Gaussian quadrature formulas.

There are many numerical methods adopted to solve mathematical problems. Early researchers focused on the methods to reduce computational costs. In recent years, reduction in computational costs makes many numerical methods available which were not tried for this reason. The use of higher order Legendre polynomials for more than 5-7 orders is usually not common. The efficient and quick numerica...

We review the methods in [4] and [24] for constructing quadratures for bandlimited exponentials and introduce a new algorithm for the same purpose. As in [4], our approach also yields generalized Gaussian quadratures for exponentials integrated against a non-sign-definite weight function. In addition, we compute quadrature weights via l and l∞ minimization and compare the corresponding quadratu...

Analysis of climate change is often computationally burdensome. Here, we present an approach for intelligently selecting a sample of climates from a population of 6800 climates designed to represent the full distribution of likely climate outcomes out to 2050 for the Zambeze River Valley. Philosophically, our approach draws upon information theory. Technically, our approach draws upon the numer...

This paper presents a reformulation of Krylov Subspace Spectral (KSS) Methods, which use Gaussian quadrature in the spectral domain compute high-order accurate approximate solutions to variable-coefficient time-dependent PDE. This reformulation reveals that KSS methods are actually high-order operator splittings that are defined implicitly, in terms of derivatives of the nodes and weights of Ga...

This paper presents a comparison of a new semi-analytical expression with Gaussian-quadrature formulas for the quasi-static double-surface potential integrals arising in the boundary integral (BI) models of micron-size objects, such as RF-MEMS switches. The integrals considered are the quasi-static Green’s functions for the scalar arid vector potentials, with constant or 96 IEEEAnfennas and Pro...

We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that ...

In environmental economics, numerical simulation using random draws is the method most commonly used to estimate joint probabilities of individual choices in discrete-choice, random-parameters models. This paper compares simulation to another method of estimation, Gaussian quadrature, on the basis of speed and accuracy. The comparison is done using stated preference data consisting of the answe...