Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0928.65032
Elliott, David
The Euler-Maclaurin formula revisited. (English)
[J] J. Aust. Math. Soc., Ser. B 40, No.E, E27-E76 (1998). ISSN 0334-2700

The author bases this paper on the conventional Euler-Maclaurin formula. The thrust of this paper is the evaluation of Cauchy principal value (CPV) integrals and for certain Hadamard finite part integrals (FPI). To this end he includes the extra term, introduced originally by the reviewer, for the CPV and differentiates the expansion, with respect to an incidental parameter, to obtain corresponding results for an FPI. He shows that the sigmoidal transformations (aka periodising transformations) are helpful in this context, and obtains discretization error estimates valid for functions belonging to a specified Sobolev space. The author points out that these results should prove particularly useful in the context of the solution of integral equations.\par Although this paper appears in the journal immediately before a companion paper [the author, ibid. Ser. B 40, No. E, E77--E137 (1998; reviewed below)] on sigmoidal functions, it should clearly be read after the companion paper.
[J.N.Lyness (Argonne)]

MSC 2000:: *65D32 Quadrature formulas (numerical methods)
65B15 Euler-Maclaurin formula
41A55 Approximate quadratures

Keywords: Euler-Maclaurin formula; sigmoidal functions; numerical integration; quadrature formulas; trapezoidal rule; Cauchy principal value integrals; Hadamard finite part integrals

Citations: Zbl 0928.65033

Cited in: Zbl 0928.65033

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]