Tractability of the Fredholm problem of the second kind

Arthur G. Werschulz & Henryk Wozniakowski
We study the tractability of computing ε-approximations of the Fredholm problem of the second kind: given f ∈ Fd and q ∈ Q2d, find u ∈ L2(Id) satisfying u(x)− q(x,y)u(y)dy=f(x) ∀x∈Id =[0,1]d. Id Here, Fd and Q2d are spaces of d-variate right hand functions and 2d-variate kernels that are continuously embedded in L2(Id) and L2(I2d), respectively. We consider the worst case setting, measuring the approximation error for the solution u in the L2 (I d...
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