Optimal approximation of elliptic problems by linear and nonlinear mappings II
نویسندگان
چکیده
منابع مشابه
Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings
We study the optimal approximation of the solution of an operator equation A(u) = f by linear mappings of rank n and compare this with the best n-term approximation with respect to an optimal Riesz basis. We consider worst case errors, where f is an element of the unit ball of a Hilbert space. We apply our results to boundary value problems for elliptic PDEs that are given by an isomorphism A :...
متن کاملOptimal approximation of elliptic problems by linear and nonlinear mappings II
We study the optimal approximation of the solution of an operator equation A(u) = f by four types of mappings: a) linear mappings of rank n; b) n-term approximation with respect to a Riesz basis; c) approximation based on linear information about the right hand side f ; d) continuous mappings. We consider worst case errors, where f is an element of the unit ball of a Sobolev or Besov space Br q...
متن کاملOptimal approximation of elliptic problems by linear and nonlinear mappings I
We study the optimal approximation of the solution of an operator equation A(u) = f by linear mappings of rank n and compare this with the best n-term approximation with respect to an optimal Riesz basis. We consider worst case errors, where f is an element of the unit ball of a Hilbert space. We apply our results to boundary value problems for elliptic PDEs that are given by an isomorphism A :...
متن کاملOptimal approximation of elliptic problems by linear and nonlinear mappings III: Frames
We study the optimal approximation of the solution of an operator equation A(u) = f by certain n-term approximations with respect to specific classes of frames. We consider worst case errors, where f is an element of the unit ball of a Sobolev or Besov space Bt q(Lp(Ω)) and Ω ⊂ Rd is a bounded Lipschitz domain; the error is always measured in the Hs-norm. We study the order of convergence of th...
متن کاملOptimal approximation of elliptic problems by linear and nonlinear mappings IV: Errors in L2 and other norms
We study the optimal approximation of the solution of an operator equation A(u) = f by linear and different types of nonlinear mappings. In our earlier papers we only considered the error with respect to a certain Hs-norm where s was given by the operator since we assumed that A : Hs 0(Ω) → H−s(Ω) is an isomorphism. The most typical case here is s = 1. It is well known that for certain regular ...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2006
ISSN: 0885-064X
DOI: 10.1016/j.jco.2006.04.001