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On the approximate minimization of functionals


Author: James W. Daniel
Journal: Math. Comp. 23 (1969), 573-581
MSC: Primary 65.30
DOI: https://doi.org/10.1090/S0025-5718-1969-0247746-7
MathSciNet review: 0247746
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Abstract: This paper considers in general the problem of finding the minimum of a given functional $ f(u)$ over a set $ B$ by approximately minimizing a sequence of functionals $ {f_n}({u_n})$ over a "discretized" set $ {B_n}$; theorems are given proving the convergence of the approximating points $ {u_n}$ in $ {B_n}$ to the desired point $ u$ in $ B$. Applications are given to the Rayleigh-Ritz method, regularization, Chebyshev solution of differential equations, and the calculus of variations.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0247746-7
Article copyright: © Copyright 1969 American Mathematical Society

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