Acta Numerica 1997 (Volume 6) - download pdf or read online

By Arieh Iserles

ISBN-10: 0521591066

ISBN-13: 9780521591065

Acta Numerica surveys every year crucial advancements in numerical research. the topics and authors, selected through a amazing foreign panel, supply a survey of articles notable of their caliber and breadth. This quantity contains articles on multivariate integration; numerical research of semiconductor units; speedy transforms in utilized arithmetic; complexity concerns in numerical research.

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P. Mysovskikh (1975), 'On Chakalov's theorem', USSR Comput. Math, and Math. Phys. 15, 221-227. I. P. Mysovskikh (1977), 'On the evaluation of integrals over the surface of a sphere', Soviet Math. Dokl. 18, 925-929. Published as I. P. Mysovskih 1977. I. P. Mysovskikh (1980), The approximation of multiple integrals by using interpolatory cubature formulae, in Quantitative Approximation (R. D. Vore and K. Scherer, eds), Academic, New York, pp. 217-243. I. P. Mysovskikh (1981), Interpolatory Cubature Formulas, Izdat.

Fig. 2. Regions S2{d2)forwhich a formula of degree 3 with 3 points exists 1 -2 -f Fig. 3. 1 Then there exists an infinite number of minimal cubature formulae of degree 2k and one (uniquely determined) minimal formula of degree Ik + 1 (both with dirndl points) for the following two classes of integrals, f(u,v)W(u,v)(u2-iv)Jdudv with a,/3 > - 1 , 7 = Proof. See Schmid and Xu (1994). Figure 3 displays Q.. Berens, Schmid and Xu (1995) obtained a similar result for arbitrary dimensions. 3. 2 and at the end of Section 5 we encountered the pleasant effect of central symmetry on cubature formulae of algebraic degree.

Appl. Math. 17, 131-149. J. N. Lyness and D. Jespersen (1975), 'Moderate degree symmetric quadrature rules for the triangle', J. Inst. Math. Appl. 15, 19-32. J. N. Lyness and B. J. J. McHugh (1970), 'On the remainder term in the Ndimensional Euler-Maclaurin expansion', Numer. Math. 15, 333-344. J. N. Lyness and G. Monegato (1980), 'Quadrature error functional expansion for the simplex when the integrand has singularities at vertices', Math. Comp. 34, 213-225. J. N. Lyness and K. K. Puri (1973), 'The Euler-Maclaurin expansion for the simplex', Math.

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Acta Numerica 1997 (Volume 6) by Arieh Iserles

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