New Methods for High-Dimensional Verified Quadrature

Reliable Computing

Volumn 5, Issue 1, 1999, Pages 13-22

  Berz, Martin ^a   Makino, Kyoko ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003019087     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026437523641     Document Type: Article

References (10)

1. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, 1983.
2. Berz, M. and Hoffstätter, G.: Computation and Application of Taylor Polynomials with Interval Remainder Bounds, Reliable Computing 4 (1) (1998), pp. 83-97.
3. Gradshteyn, I. S. and Ryzhik, I. M.: Table of Integrals, Series, and Products, Academic Press, New York, 1980.
4. Kaucher, E. W. and Miranker, W. L.: Self-Validating Numerics for Function Space Problems: Computation with Guarantees for Differential and Integral Equations, Academic Press, New York, 1984.
5. Kearfott, R. B. and Kreinovich, V. (eds): Applications of Interval Computations, Kluwer Academic Publisher, 1996.
6. Makino, K.: Rigorous Analysis of Nonlinear Motion in Particle Accelerators, PhD thesis, Michigan State University, East Lansing, Michigan, USA, 1998. also MSUCL-1093.
7. Makino, K. and Berz, M.: Remainder Differential Algebras and Their Applications, in: Berz, M., Bischof, C., Corliss, G., and Griewank, A. (eds), Computational Differentiation: Techniques, Applications, and Tools, SIAM, 1996, pp. 63-74.
8. Makino, K and Berz, M.: Efficient Control of the Dependency Problem Based on Taylor Model Methods, Reliable Computing, this volume, pp. 3-12.
9. Moore, R. E.: Methods and Applications of Interval Analysis, SIAM, 1979.
10. Storck, U.: Numerical Integration in Two Dimensions with Automatic Result Verification, in: Adams, E. and Kulisch, U. (eds), Scientific Computing with Automatic Result Verification, Academic Press, 1993, pp. 187-224.