A Gaussian quadrature rule for oscillatory integrals on a bounded interval
Discrete & Continuous Dynamical Systems - A, 2014 We investigate a Gaussian quadrature rule and the corresponding orthogonal polynomials for the oscillatory weight function $e^{iωx}$ on the interval $[-1,1]$. We show that such a rule attains high asymptotic order, in the sense that the quadrature error quickly decreases as a function of the frequency $ω$. However, accuracy is maintained for all values
Asheim, Andreas +3 more
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On relation between one multiple and a corresponding one-dimensional integral with applications [PDF]
Yugoslav Journal of Operations Research, 2018 For a given finite positive measure on an interval I ⊆ R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced.
Bajić Tatjana
doaj +1 more source
Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals [PDF]
Mathematical Methods in the Applied Sciences, 2020 Inspired with papers by Bokhari, Qadir, and Al‐Attas (2010) and by Rapaić, Šekara, and Govedarica (2014), in this paper we investigate a few types of orthogonal polynomials on finite intervals and derive the corresponding quadrature formulas of Gaussian type for efficient numerical computation of the left and right fractional Riemann‐Liouville ...
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High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: $\mathcal{O}(1)$ Sampling Cost via Incident-Field Windowing and Recentering [PDF]
, 2020 This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains.
Anderson, Thomas G. +2 more
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OPERATOR METHOD IN THE SCALAR WAVE DIFFRACTION BY AXIALLY-SYMMETRIC DISCONTINUITIES IN THE SCREEN
Radio Physics and Radio Astronomy, 2018 Purpose: The scalar wave diffraction by the annular slot in an infinitely thin screen is considered in case of Dirichlet and Neumann boundary conditions. Diffraction problem by a flat ring is also considered as a dual one.
M. E. Kaliberda +2 more
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Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification [PDF]
, 2014 Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits.
Daniel, Luca +4 more
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The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC [PDF]
, 2014 Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the ...
Inghelbrecht, Veronique +3 more
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Smoothing the payoff for efficient computation of Basket option prices [PDF]
, 2016 We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth ...
Bayer, Christian +2 more
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On the convergence of spectral deferred correction methods [PDF]
, 2018 In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266].
Causley, Mathew F., Seal, David C.
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Introduction to Random Signals and Noise [PDF]
, 2006 Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired ...
Etten, Wim van
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