An intractability result for multiple integration

作者：Ian H. Sloan, H. Woźniakowski · 发表于：Mathematics of Computation · 年份：1997 · DOI：10.1090/s0025-5718-97-00834-x · 被引用次数：34 · 研究领域：Mathematical Approximation and Integration、Cryptography and Residue Arithmetic、Matrix Theory and Algorithms

We prove that the problem of multiple integration in the Korobov class E α , d E_{\alpha ,d} is intractable since the number of function evaluations required to achieve a worst case error less than 1 1 is exponential in the dimension.