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Titlebook: Numerical Integration; Recent Developments, Patrick Keast,Graeme Fairweather Book 1987 D. Reidel Publishing Company, Dordrecht, Holland 198

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书目名称Numerical Integration
副标题Recent Developments,
编辑Patrick Keast,Graeme Fairweather
视频video
丛书名称Nato Science Series C:
图书封面Titlebook: Numerical Integration; Recent Developments, Patrick Keast,Graeme Fairweather Book 1987 D. Reidel Publishing Company, Dordrecht, Holland 198
描述This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled ‘Numerical Integration: Recent Developments, Software and Applications‘, held at Dalhousie University, Halifax, Canada, August 11-15, 1986. The Workshop was attended by thirty-six scientists from eleven NATO countries. Thirteen invited lectures and twenty-two contributed lectures were presented, of which twenty-five appear in full in this volume, together with extended abstracts of the remaining ten. It is more than ten years since the last workshop of this nature was held, in Los Alamos in 1975. Many developments have occurred in quadrature in the intervening years, and it seemed an opportune time to bring together again researchers in this area. The development of QUADPACK by Piessens, de Doncker, Uberhuber and Kahaner has changed the focus of research in the area of one dimensional quadrature from the construction of new rules to an emphasis on reliable robust software. There has been a dramatic growth in interest in the testing and evaluation of software, stimulated by the work of Lyness and Kaganove, Einarsson, and Piessens. The earlier research of Pa
出版日期Book 1987
关键词Approximation; algorithms; classification; computer; optimization
版次1
doihttps://doi.org/10.1007/978-94-009-3889-2
isbn_softcover978-94-010-8227-3
isbn_ebook978-94-009-3889-2Series ISSN 1389-2185
issn_series 1389-2185
copyrightD. Reidel Publishing Company, Dordrecht, Holland 1987
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Fast Generation of Quadrature Rules with Some Special Propertiess derived from approximations to . generated by implicit linear multistep formulae. Suitable “starting” weights, computed using the Björck-Pereyra algorithm and FFT techniques, produce formulae with good order accuracy for functions φ(.) of the form .. The discussion is associated with FORTRAN 77 code given in [2].
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Approximate Computation of Strongly Oscillatory Integrals with Compound Precisions periodic of period unity in ., and λ is a large parameter. It is shown that there can be found a class of quadrature formulas which possess any preassigned compound precision [.,λ.]. Moreover, the results announced in our abstract [6] are refined and improved.
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978-94-010-8227-3D. Reidel Publishing Company, Dordrecht, Holland 1987
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Modified Clenshaw-Curtis Integration and Applications to Numerical Computation of Integral TransformThe main difficulty in using modified Clenshaw-Curtis integration for computing Singular and oscillatory integrals is the computation of the modified moments. In this paper we give recurrence formulae for computing modified moments for a number of important weight functions.
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Indefinite Integration Formulas Based on the Sinc ExpansionThe “Tanh rule” of C. Schwartz approximates . by ., where . = .(.) is given by a certain formula; .. This integration rule has been shown to be remarkably accurate. Its error is . for some . > 0 even when the integrand is infinite at an endpoint of the integration interval.
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Quadrature Rules with End-Point Corrections: Comments on a Paper by Garloff, Solak and SzydelkoGarloff, Solak and Szydelko [1] have proposed a modified trapezoidal rule quadrature with correction terms involving two points outside the range of integration. The rule is exact for cubics. We show:
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