<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "On the Curse of Dimensionality in the Ritz Method"^^ . "It is shown that the classical Ritz method of the calculus of variations suffers from the “curse of dimensionality,” i.e., an exponential growth, as a function of the number of variables, of the dimension a linear subspace needs in order to achieve a desired relative improvement in the accuracy of approximation of the optimal solution value. The proof is constructive and is obtained by exhibiting a family of infinite-dimensional optimization problems for which this happens, namely those with quadratic functional and spherical constraint. The results provide a theoretical motivation for the search of alternative solution methods, such as the so-called “extended Ritz method,” to deal with the curse of dimensionality."^^ . "2016" . "168" . "2" . . "Springer"^^ . . . "Journal of Optimization Theory and Applications"^^ . . . "00223239" . . . . . . . "Giorgio"^^ . "Gnecco"^^ . "Giorgio Gnecco"^^ . . . . . "HTML Summary of #3123 \n\nOn the Curse of Dimensionality in the Ritz Method\n\n" . "text/html" . . . "QA75 Electronic computers. Computer science"@en . .