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The randomized complexity of initial value problems
We study the complexity of randomized solution of initial value problems for systems of ordinary differential equations for which the input data are assumed to be @c-smooth (@[email protected]: the rth derivatives satisfy a @r-Holder condition). Expand
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The randomized complexity of indefinite integration
We show that for functions [email protected]?L"p([0,1]^d), the family of integrals @!"["0","x"]f(t)dt(x=(x"1,...,x"d)^d) can be approximated by a randomized algorithm uniformly over the indefinite integral, the anti-derivative. We also prove lower bounds and discuss the dependence of the constants in the error estimates on the dimension. Expand
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