Integrating composed singularities using nonuniform subdivision and extrapolation

Singstad, Kristoffer; Espelid, Terje O.

doi:10.1016/s0377-0427(99)00227-7

Journal of Computational and Applied Mathematics

1999

DOI: 10.1016/s0377-0427(99)00227-7

|View full text |Cite

Integrating composed singularities using nonuniform subdivision and extrapolation

Kristoffer Singstad¹,

Terje O. Espelid²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2003

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

SINGINT: Automatic numerical integration of singular integrands

Kauer

2003

Computer Physics Communications

View full text Add to dashboard Cite

We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion and are runtime and memory optimised, respectively. SINGINT, a C implementation of the algorithms, is introduced and its utilisation in the calculation of particle scattering amplitudes is exemplified.Comment: 15 pages, 1 figur

show abstract

SINGINT: Automatic numerical integration of singular integrands

Kauer

2003

Computer Physics Communications

View full text Add to dashboard Cite

show abstract

A numerical evaluation of the scalar hexagon integral in the physical region

2003

View full text Add to dashboard Cite

We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative corrections to multi-particle cross sections. The hexagon integral is represented in terms of n-dimensional triangle functions and (n+2)-dimensional box functions. If infrared poles are present this representation naturally splits into a finite and a pole part. For a fast numerical integration of the finite part we propose simple one-and two-dimensional integral representations. We set up an iterative numerical integration method to calculate these integrals directly in an efficient way. The method is illustrated by explicit results for pentagon and hexagon functions with some generic physical kinematics.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Integrating composed singularities using nonuniform subdivision and extrapolation

Cited by 2 publications

References 14 publications

SINGINT: Automatic numerical integration of singular integrands

SINGINT: Automatic numerical integration of singular integrands

A numerical evaluation of the scalar hexagon integral in the physical region

Contact Info

Product

Resources

About