Expected uniform integration approximation under general equal measure partition
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In this paper, we study bounds of expected L_2-discrepancy to give mean square error of uniform integration approximation for functions in Sobolev space ℋ^1(K), where ℋ is a reproducing Hilbert space with kernel K. Better order O(N^-1-1/d) of approximation error is obtained, comparing with previously known rate O(N^-1) using crude Monte Carlo method. Secondly, we use expected L_p-discrepancy bound(p≥ 1) of stratified samples to give several upper bounds of p-moment of integral approximation error in general Sobolev space F_d,q^*.
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