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Local error estimates and regularity tests for the implementation of double adaptive quadrature
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Source ACM Transactions on Mathematical Software (TOMS) archive
Volume 23 ,  Issue 1  (March 1997) table of contents
Pages: 16 - 31  
Year of Publication: 1997
ISSN:0098-3500
Authors
Paola Favati  IMC-CNR, Pisa, Italy
Giuseppe Fiorentino  Univ. of Pisa, Pisa, Italy
Grazia Lotti  Univ. of Parma, Parma, Italy
Francesco Romani  Univ. of Pisa, Pisa, Italy
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 3,   Downloads (12 Months): 29,   Citation Count: 0
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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

1
Jarle Berntsen , Terje O. Espelid, Error estimation in automatic quadrature routines, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.233-252, June 1991  [doi>10.1145/108556.108575]
 
2
DAVIS, P. AND RABINOWITZ, P. 1984. Methods of Numerical Integration. Academic Press, New York.
 
3
Paola Favati , Grazia Lotti , Gaspare Di Marco , Francesco Romani, Asymptotic behavior of automatic quadrature, Journal of Complexity, v.10 n.3, p.296-340, Sept. 1994  [doi>10.1006/jcom.1994.1016]
4
Paola Favati , Grazia Lotti , Francesco Romani, Interpolatory integration formulas for optimal composition, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.207-217, June 1991  [doi>10.1145/108556.108571]
5
Paola Favati , Grazia Lotti , Francesco Romani, Algorithm 691; Improving QUADPACK automatic integration routines, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.218-232, June 1991  [doi>10.1145/108556.108580]
 
6
FAVATI, P., LOTTI, G., AND ROMANI, F. 1992. Asymptotic expansion of error in interpolatory quadrature. Comput. Math. Appl. 24, 99-104.
 
7
LYNESS, g. N. AND KAGANOVE, g.g. 1977. A technique for comparing automatic quadrature routines. Comput. J. 20, 170-177.
 
8
PIESSENS, R., DE DONCKER-KAPENGA, E., UBERHUBER, C., AND KAHANER, D.K. 1983. QUAD- PACK: A Subroutine Package for Automatic Integration. Springer, Berlin.
 
9
Hiroshi Sugiura , Tetsuya Sakurai, On the construction of high-order integration formulae for the adaptive quadrature method, Journal of Computational and Applied Mathematics, v.28 n.1989, p.367-381, December 1989  [doi>10.1016/0377-0427(89)90348-8]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Adaptive and iterative quadrature

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Reliability and robustness; Efficiency


General Terms:
Algorithms


Keywords:
automatic integration, error estimates, local quadrature


REVIEW

"Alan Charles Genz : Reviewer"

An important problem associated with numerical integration software is that of error estimation. It is difficult to compute error estimates that are both reliable and accurate, and this difficulty increases with the use of high-order local int  more...

Collaborative Colleagues:
Paola Favati: colleagues
Giuseppe Fiorentino: colleagues
Grazia Lotti: colleagues
Francesco Romani: colleagues

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