An intractability result for multiple integration

Mathematics of Computation

Volumn 66, Issue 219, 1997, Pages 1119-1124

  Sloan, I H ^a   Wozniakowski H ^a  

^a NONE

Author keywords

Intractability; Lattice rules; Multiple integration

Indexed keywords

EID: 0038967057     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-97-00834-x     Document Type: Article

References (9)

1. Disney, S.A.R. Error bounds for rank 1 lattice quadrature rules modulo composites. Monatshefte für Mathematik, 110, 89-100 (1990). MR 91m:65067
2. Disney, S.A.R. and Sloan, I.H. Error bounds for the method of good lattice points. Mathematics of Computation, 56, 257-66 (1991). MR 91m:65068
3. Disney, S.A.R. and Sloan, I.H., Lattice integration rules of maximal rank formed by copying rank 1 rules, SIAM Journal on Numerical Analysis, 29, 566-77 (1992). MR 92k:65034
4. Hua, L. K. and Wang, Y., Applications of number theory to numerical analysis. Springer Verlag, Berlin (1981). MR 83g:10034
5. Niederreiter, H. Random number generation and quasi-Monte Carlo methods. Society for Industrial and Applied Mathematics, Philadelphia (1992). MR 93h:65008
6. Sharygin, I. F., A lower estimate for the error of quadrature formulas for certain classes of functions (in Russian), Zh. Vychisl. Mat. i Mat. Fiz., 3, 370-376 (1963).
7. Sloan, I.H. and Joe, S. Lattice methods for multiple integration. Oxford University Press, Oxford (1994).
8. Sloan, I.H. and Kachoyan, P.J. Lattice methods for multiple integration: theory, error analysis and examples. SIAM Journal on Numerical Analysis, 24, 116-28 (1987). MR 88e:65023
9. Traub, J.F., Wasilkowski, G. and Woźniakowski, H. Information-based complexity. Academic Press, Boston (1988). MR 90f:68085