Optimal approximation of elliptic problems by linear and nonlinear mappings I

• DOI: 10.1016/j.jco.2005.06.005
• Publication Date: 2005-09-09T15:52:05Z
• Authors: Stephan Dahlke; Erich Novak; Winfried Sickel
• Keywords: Unit sphere; Elliptic operator

We study the optimal approximation of the solution of an operator equation Au=f by linear and nonlinear mappings. We identify those cases where optimal nonlinear approximation is better than optimal linear approximation.<br/>Journal of Complexity, to appear. It is a long paper: 69 pages<br/>