Abstract
In this chapter some facts from interpolation are used. Therefore, the reader may 3 first have a look at §4.1 of the next chapter, which is devoted to interpolation. We 4 prefer to start with quadrature instead of interpolation, since a projection between 5 function spaces (interpolation) is more involved than a functional (quadrature).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bulirsch, R.: Bemerkungen zur Romberg-Integration. Numer. Math. 6, 6–16 (1964)
Christoffel, E.B.: Über die Gaußische Quadratur und eine Verallgemeinerung derselben. J. Reine Angew. Math. 55, 61–82 (1858)
Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration, 2nd ed. Academic Press, New York (1984)
Gauss, C.F.: Methodus nova integralium valores per approximationem inveniendi. In: Werke, vol. 3, pp. 163–196. K. Gesellschaft Wissenschaft, Göttingen (1876). (reprint by Georg Olms, Hildesheim, 1981)
Natanson, I.P.: Konstruktive Funktionentheorie. Akademie-Verlag, Berlin (1955)
Ouspensky, J.V.: Sur les valeurs asymptotiques des coefficients de Cotes. Bull. Amer. Math. Soc. 31, 145–156 (1925)
Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics, 2nd ed. Springer, Berlin (2007)
Romberg, W.: Vereinfachte numerische Quadratur. Norske Vid. Selsk. Forh. [Proceedings of the Royal Norwegian Society of Sciences and Letters], Trondheim 28, 30–36 (1955)
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. North-Holland, Amsterdam (1980)
Stroud, A., Secrest, D.: Gaussian Quadrature Formulas. Prentice-Hall, Englewood Cliffs (1966)
Whiteside, D.T. (ed.): The mathematical papers of Isaac Newton, Vol. 4. Cambridge University Press, Cambridge (1971)
Yosida, K.: Functional Analysis. Springer, New York (1968)
Zeidler, E. (ed.): Oxford Users’ Guide to Mathematics. Oxford University Press, Oxford (2004)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hackbusch, W. (2014). Quadrature. In: The Concept of Stability in Numerical Mathematics. Springer Series in Computational Mathematics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39386-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-39386-0_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39385-3
Online ISBN: 978-3-642-39386-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)