Error Estimates for Approximate Optimization by the Extended Ritz Method
نویسندگان
چکیده
منابع مشابه
Error Estimates for Approximate Optimization by the Extended Ritz Method
An alternative to the classical Ritz method of approximate optimization is investigated. In the extended Ritz method, sets of admissible solutions are approximated by their intersections with linear combinations of n-tuples from a given set. This approximation scheme, called variable-basis approximation, includes functions computable by trigonometric polynomials with free frequencies, neural ne...
متن کاملTo Appear in Siam Journal on Optimization, 2004 Error Estimates for Approximate Optimization by the Extended Ritz Method
An alternative to the classical Ritz method for approximate optimization is investigated. In the extended Ritz method, sets of admissible solutions are approximated by their intersections with sets of linear combinations of all n-tuples of functions from a given basis. This alternative scheme, called variable-basis approximation, includes functions computable by trigonometric polynomials with f...
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Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as ...
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The following estimate for the Rayleigh–Ritz method is proved: |λ̃−λ||(ũ,u)| ≤ ‖Aũ− λ̃ũ‖sin∠{u;Ũ}, ‖u‖= 1. Here A is a bounded self-adjoint operator in a real Hilbert/euclidian space, {λ,u} one of its eigenpairs, Ũ a trial subspace for the Rayleigh–Ritz method, and {λ̃, ũ} a Ritz pair. This inequality makes it possible to analyze the fine structure of the error of the Rayleigh–Ritz method, in part...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2005
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623403426507