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Near-optimal approximation methods for elliptic PDEs with lognormal coefficients

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Figure 5.1 shows the growth of the largest (component of the) indices of the Hermite polynomials associated to the random variables y 0,0 , y 1,0 , y 2,0 , y 3,0 that multiply the first four levels of the Schauder basis ψ 0,0 , ψ 1,0 , ψ 2,0 , ψ 3,0 in (4.
Figure 5.2: Some sections of the set Λ n with n = 4000 and β = 1 2 .

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