Quadpack

Piessens, Robert; Doncker-Kapenga, Elise de; Überhuber, Christoph; Kahaner, David K.

doi:10.1007/978-3-642-61786-7

Cited by 520 publications

(160 citation statements)

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“…Results have been tested both within Mathematica 10 [37] and in C++ using the Gauss-Kronrod algorithm from the Quadpack library [38]. The following checks were carried out for the U 4 and U 5 master integrals: at least ten digits agreement were obtained…”

Section: Numerical Integration and Checksmentioning

confidence: 99%

Three-loop vacuum integrals with arbitrary masses

Freitas

2016

J. High Energ. Phys.

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Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, analytical results for integrals with only one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.

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Section: Numerical Integration and Checksmentioning

confidence: 99%

Three-loop vacuum integrals with arbitrary masses

Freitas

2016

J. High Energ. Phys.

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“…The non-singular and Cauchy principle value integrals (which occurred in the computation of the pressure distribution in Figure 2) were evaluated with two computer programs DQAG and DQAWC from QUADPACK [19] which employ adaptive schemes.…”

Section: Discussionmentioning

confidence: 99%

A flat ship theory on bow and stern flows

Zhu

Zhang

2003

ANZIAM J.

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An analytical solution of a two-dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell's thin ship theory and leads to a mixed initial-boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener-Hopf technique and closed-form far-field results are obtained for an arbitrary hull shape. Apart from providing a better understanding of the underlying physics, the newly found analytical solution has shed some light on solving a longtime outstanding problem in the engineering practice of ship building, the optimisation of hull shape.

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“…However, using available fast and accurate algorithms for the one-dimensional integration makes the fitting still practical. In this work we have used a globally adaptive integration scheme documented in Piessens et al (1983). The maximization of (11) is subject to constraints to satisfy the requirement that the correlation matrix Σ is positive definite.…”

Section: Maximum Likelihoodmentioning

confidence: 99%

Thetcopula with multiple parameters of degrees of freedom: bivariate characteristics and application to risk management

Luo

Shevchenko

2010

Quantitative Finance

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The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula can be significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall.

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Quadpack

Cited by 520 publications

References 0 publications

Three-loop vacuum integrals with arbitrary masses

Three-loop vacuum integrals with arbitrary masses

A flat ship theory on bow and stern flows

Thetcopula with multiple parameters of degrees of freedom: bivariate characteristics and application to risk management

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