Some results on the complexity of numerical integration

Abstract

We present some results on the complexity of numerical integration. We start with the seminal paper of Bakhvalov (1959) and end with new results on the curse of dimensionality and on the complexity of oscillatory integrals. This survey paper consists of four parts: 1. Classical results till 1971 2. Randomized algorithms 3. Tensor product problems, tractability and weighted norms 4. Some recent results: Ck functions and oscillatory integrals.