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- W2025559620 abstract "We study the information complexity in the randomized setting of solving a general elliptic PDE of order 2m in a smooth, bounded domain Q⊂Rd with smooth coefficients and homogeneous boundary conditions. The solution is sought on a smooth submanifold M⊆Q of dimension 0⩽d1⩽d, the right-hand side is supposed to be in Cr(Q), the error is measured in the L∞(M) norm. We show that the nth minimal error is (up to logarithmic factors) of ordern-min(r+2m)/d1,r/d+1/2.For comparison, in the deterministic setting the nth minimal error is of order n-r/d, for all d1." @default.
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- W2025559620 date "2006-04-01" @default.
- W2025559620 modified "2023-10-17" @default.
- W2025559620 title "The randomized information complexity of elliptic PDE" @default.
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- W2025559620 doi "https://doi.org/10.1016/j.jco.2005.11.003" @default.
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