Optimal approximation of elliptic problems by linear and nonlinear mappings I
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 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 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 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.2005.06.005